Dissertations / Theses on the topic 'Functional data analysis'
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Yao, Fang. "Functional data analysis for longitudinal data /." For electronic version search Digital dissertations database. Restricted to UC campuses. Access is free to UC campus dissertations, 2003. http://uclibs.org/PID/11984.
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Hadjipantelis, Pantelis-Zenon. "Functional data analysis in phonetics." Thesis, University of Warwick, 2013. http://wrap.warwick.ac.uk/62527/.
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The study of speech sounds has established itself as a distinct area of research, namely Phonetics. This is because speech production is a complex phenomenon mediated by the interaction of multiple components of a linguistic and non-linguistic nature. To investigate such phenomena, this thesis employs a Functional Data Analysis framework where speech segments are viewed as functions. FDA treats functions as its fundamental unit of analysis; the thesis takes advantage of this, both in conceptual as well as practical terms, achieving theoretical coherence as well as statistical robustness in its insights. The main techniques employed in this work are: Functional principal components analysis, Functional mixed-effects regression models and phylogenetic Gaussian process regression for functional data. As it will be shown, these techniques allow for complementary analyses of linguistic data. The thesis presents a series of novel applications of functional data analysis in Phonetics. Firstly, it investigates the influence linguistic information carries on the speech intonation patterns. It provides these insights through an analysis combining FPCA with a series of mixed effect models, through which meaningful categorical prototypes are built. Secondly, the interplay of phase and amplitude variation in functional phonetic data is investigated. A multivariate mixed effects framework is developed for jointly analysing phase and amplitude information contained in phonetic data. Lastly, the phylogenetic associations between languages within a multi-language phonetic corpus are analysed. Utilizing a small subset of related Romance languages, a phylogenetic investigation of the words' spectrograms (functional objects defined over two continua simultaneously) is conducted to showcase a proof-of-concept experiment allowing the interconnection between FDA and Evolutionary Linguistics.
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Bacchetti, Enrico <1997>. "Functional Data Analysis - An application to weather data." Master's Degree Thesis, Università Ca' Foscari Venezia, 2021. http://hdl.handle.net/10579/19503.
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The goal of this project is to introduce the topic of Functional Data Analysis (FDA) a relative new research area that resembles and puts together different fields and sectors, such as Statistics, Econometrics, Machine Learning, ... Actually, it can be considered a branch of Statistics.
Functional Data Analysis was developed in order to address some data analysis problem, especially for what concerns phenomena that show, by nature, a relative ”smooth” behavior, i.e. that can be represented by curves that present some sort of regularity, and that varies over a continuum.
My work has been articulated in the following manner: the first Chapter (1) is dedicated to the main and must-known theory necessary for understanding what FDA is and what kind of works can be devised using its particular techniques. Chapter 2 presents the data that are deployed in carrying out my empirical analysis and in particular: the type of data with all their characteristics, the preliminary analysis through which data has been processed in order to clean and finalize them. The third Chapter (3) contains the empirical analysis and includes all the graphs and plots that are helpful to understand the results achieved. Finally, Chapter 4 is devoted to conclusion and remarks and provide hints for developing further the work. As for the empirical part, I have focused my attention on weather and climate and in particular on daily temperature and precipitation amounts related to 30 different weather stations in Europe.
As for the code part, nowadays many packages or toolboxes for different languages (R, MATLAB, python) have been devised by practitioners aiming to address all the complexity of functional data analysis. In my application, I have opted for using MATLAB and in particular the FDA Toolbox.
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Lee, Ho-Jin. "Functional data analysis: classification and regression." Texas A&M University, 2004. http://hdl.handle.net/1969.1/2805.
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Functional data refer to data which consist of observed functions or curves evaluated
at a finite subset of some interval. In this dissertation, we discuss statistical
analysis, especially classification and regression when data are available in function
forms. Due to the nature of functional data, one considers function spaces in presenting
such type of data, and each functional observation is viewed as a realization
generated by a random mechanism in the spaces. The classification procedure in
this dissertation is based on dimension reduction techniques of the spaces. One commonly
used method is Functional Principal Component Analysis (Functional PCA) in
which eigen decomposition of the covariance function is employed to find the highest
variability along which the data have in the function space. The reduced space of
functions spanned by a few eigenfunctions are thought of as a space where most of the
features of the functional data are contained. We also propose a functional regression
model for scalar responses. Infinite dimensionality of the spaces for a predictor causes
many problems, and one such problem is that there are infinitely many solutions. The
space of the parameter function is restricted to Sobolev-Hilbert spaces and the loss
function, so called, e-insensitive loss function is utilized. As a robust technique of
function estimation, we present a way to find a function that has at most e deviation
from the observed values and at the same time is as smooth as possible.
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Zoglat, Abdelhak. "Analysis of variance for functional data." Thesis, University of Ottawa (Canada), 1994. http://hdl.handle.net/10393/10136.
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In this dissertation we present an extension to the well known theory of multivariate analysis of variance. In various situations data are continuous stochastic functions of time or space. The speed of pollutants diffusing through a river, the real amplitude of a signal received from a broadcasting satellite, or the hydraulic conductivity rates at a given region are examples of such processes. After the mathematical background we develop tools for analyzing such data. Namely, we develop estimators, tests, and confidence sets for the parameters of interest. We extend these results, obtained under the normality assumption, and show that they are still valid if this assumption is relaxed. Some examples of applications of our techniques are given. We also outline how the latter can apply to random and mixed models for continuous data. In the appendix, we give some programs which we use to compute the distributions of some of our tests statistics.
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Friman, Ola. "Adaptive analysis of functional MRI data /." Linköping : Univ, 2003. http://www.bibl.liu.se/liupubl/disp/disp2003/tek836s.pdf.
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Martinenko, Evgeny. "Functional Data Analysis and its application to cancer data." Doctoral diss., University of Central Florida, 2014. http://digital.library.ucf.edu/cdm/ref/collection/ETD/id/6323.
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The objective of the current work is to develop novel procedures for the analysis of functional data and apply them for investigation of gender disparity in survival of lung cancer patients. In particular, we use the time-dependent Cox proportional hazards model where the clinical information is incorporated via time-independent covariates, and the current age is modeled using its expansion over wavelet basis functions. We developed computer algorithms and applied them to the data set which is derived from Florida Cancer Data depository data set (all personal information which allows to identify patients was eliminated). We also studied the problem of estimation of a continuous matrix-variate function of low rank. We have constructed an estimator of such function using its basis expansion and subsequent solution of an optimization problem with the Schattennorm penalty. We derive an oracle inequality for the constructed estimator, study its properties via simulations and apply the procedure to analysis of Dynamic Contrast medical imaging data.Ph.D.
Doctorate
Mathematics
Sciences
Mathematics
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Kröger, Viktor. "Classification in Functional Data Analysis : Applications on Motion Data." Thesis, Umeå universitet, Institutionen för matematik och matematisk statistik, 2021. http://urn.kb.se/resolve?urn=urn:nbn:se:umu:diva-184963.
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Anterior cruciate knee ligament injuries are common and well known, especially amongst athletes.These injuries often require surgeries and long rehabilitation programs, and can lead to functionloss and re-injuries (Marshall et al., 1977). This work aims to explore the possibility of applyingsupervised classification on knee functionality, using different types of models, and testing differentdivisions of classes. The data used is gathered through a performance test, where individualsperform one-leg hops with motion sensors attached to their bodies. The obtained data representsthe position over time, and is considered functional data.With functional data analysis (FDA), a process can be analysed as a continuous function of time,instead of being reduced to finite data points. FDA includes many useful tools, but also somechallenges. A functional observation can for example be differentiated, a handy tool not found inthe multivariate tool-box. The speed, and acceleration, can then be calculated from the obtaineddata. How to define "similarity" is, on the other hand, not as obvious as with points. In this work,an FDA-approach is taken on classifying knee kinematic data, from a long-term follow-up studyon knee ligament injuries.This work studies kernel functional classifiers, and k-nearest neighbours models, and performssignificance tests on the model accuracy, using re-sampling methods. Additionally, depending onhow similarity is defined, the models can distinguish different features of the data. Attempts atutilising more information through incorporation of ensemble-methods, does not exceed the singlemodels it is created from. Further, it is shown that classification on optimised sub-domains, canbe superior to classifiers using the full domain, in terms of predictive power.Främre korsbandsskador är vanliga och välkända skador, speciellt bland idrottsutövare. Skadornakräver ofta operationer och långa rehabiliteringsprogram, och kan leda till funktionell nedsättningoch återskador (Marshall et al., 1977). Målet med det här arbetet är att utforska möjligheten attklassificera knän utifrån funktionalitet, där utfallet är känt. Detta genom att använda olika typerav modeller, och genom att testa olika indelningar av grupper. Datat som används är insamlatunder ett prestandatest, där personer hoppat på ett ben med rörelsesensorer på kroppen. Deninsamlade datan representerar position över tid, och betraktas som funktionell data.Med funktionell dataanalys (FDA) kan en process analyseras som en kontinuerlig funktion av tid,istället för att reduceras till ett ändligt antal datapunkter. FDA innehåller många användbaraverktyg, men även utmaningar. En funktionell observation kan till exempel deriveras, ett händigtverktyg som inte återfinns i den multivariata verktygslådan. Hastigheten och accelerationen kandå beräknas utifrån den insamlade datan. Hur "likhet" är definierat, å andra sidan, är inte likauppenbart som med punkt-data. I det här arbetet används FDA för att klassificera knärörelsedatafrån en långtidsuppföljningsstudie av främre korsbandsskador.I detta arbete studeras både funktionella kärnklassificerare och k-närmsta grannar-metoder, och ut-för signifikanstest av modellträffsäkerheten genom omprovtagning. Vidare kan modellerna urskiljaolika egenskaper i datat, beroende på hur närhet definieras. Ensemblemetoder används i ett försökatt nyttja mer av informationen, men lyckas inte överträffa någon av de enskilda modellerna somutgör ensemblen. Vidare så visas också att klassificering på optimerade deldefinitionsmängder kange en högre förklaringskraft än klassificerare som använder hela definitionsmängden.
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Alshabani, Ali Khair Saber. "Statistical analysis of human movement functional data." Thesis, University of Nottingham, 2005. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.421478.
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Prentius, Wilmer. "Exploring Cumulative Incomefunctions by Functional Data Analysis." Thesis, Umeå universitet, Statistik, 2016. http://urn.kb.se/resolve?urn=urn:nbn:se:umu:diva-122685.
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Cumulative incomes can be seen as the added yearly incomes for some distinct amount of years. It can also be thought of as a continuous curve, where income continuously flows into ones account. The analyzing of curves, or functions, instead of uni- or multivariate data, needs and enables different approaches. In this thesis, methods called Functional Data Analysis are used to show how analyzes of such cumulative income curves can be done, mainly through functional adaptions of principal component analysis and linear regression. Results shows how the smoothing of curves helps to decrease variances in a bias-variance trade-off, while having problems accounting for data containing many low valued observations. Furthermore, results indicates that education might have an effect, when controlling for employment rate, in the sample.
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Benko, Michal. "Functional data analysis with applications in finance." Doctoral thesis, Humboldt-Universität zu Berlin, Wirtschaftswissenschaftliche Fakultät, 2007. http://dx.doi.org/10.18452/15585.
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An vielen verschiedenen Stellen der angewandten Statistik sind die zu untersuchenden Objekte abhängig von stetigen Parametern. Typische Beispiele in Finanzmarktapplikationen sind implizierte Volatilitäten, risikoneutrale Dichten oder Zinskurven. Aufgrund der Marktkonventionen sowie weiteren technisch bedingten Gründen sind diese Objekte nur an diskreten Punkten, wie zum Beispiel an Ausübungspreise und Maturitäten, für die ein Geschäft in einem bestimmten Zeitraum abgeschlossen wurde, beobachtbar. Ein funktionaler Datensatz ist dann vorhanden, wenn diese Funktionen für verschiedene Zeitpunkte (z.B. Tage) oder verschiedene zugrundeliegende Aktiva gesammelt werden. Das erste Thema, das in dieser Dissertation betrachtet wird, behandelt die nichtparametrischen Methoden der Schätzung dieser Objekte (wie z.B. implizierte Volatilitäten) aus den beobachteten Daten. Neben den bekannten Glättungsmethoden wird eine Prozedur für die Glättung der implizierten Volatilitäten vorgeschlagen, die auf einer Kombination von nichtparametrischer Glättung und den Ergebnissen der arbitragefreien Theorie basiert. Der zweite Teil der Dissertation ist der funktionalen Datenanalyse (FDA), speziell im Zusammenhang mit den Problemen, der empirischen Finanzmarktanalyse gewidmet. Der theoretische Teil der Arbeit konzentriert sich auf die funktionale Hauptkomponentenanalyse -- das funktionale Ebenbild der bekannten Dimensionsreduktionstechnik. Ein umfangreicher überblick der existierenden Methoden wird gegeben, eine Schätzmethode, die von der Lösung des dualen Problems motiviert ist und die Zwei-Stichproben-Inferenz basierend auf der funktionalen Hauptkomponentenanalyse werden behandelt. Die FDA-Techniken sind auf die Analyse der implizierten Volatilitäten- und Zinskurvendynamik angewandt worden. Darüber hinaus, wird die Implementation der FDA-Techniken zusammen mit einer FDA-Bibliothek für die statistische Software Xplore behandelt.In many different fields of applied statistics an object of interest is depending on some continuous parameter. Typical examples in finance are implied volatility functions, yield curves or risk-neutral densities. Due to the different market conventions and further technical reasons, these objects are observable only on a discrete grid, e.g. for a grid of strikes and maturities for which the trade has been settled at a given time-point. By collecting these functions for several time points (e.g. days) or for different underlyings, a bunch (sample) of functions is obtained - a functional data set. The first topic considered in this thesis concerns the strategies of recovering the functional objects (e.g. implied volatilities function) from the observed data based on the nonparametric smoothing methods. Besides the standard smoothing methods, a procedure based on a combination of nonparametric smoothing and the no-arbitrage-theory results is proposed for implied volatility smoothing. The second part of the thesis is devoted to the functional data analysis (FDA) and its connection to the problems present in the empirical analysis of the financial markets. The theoretical part of the thesis focuses on the functional principal components analysis -- functional counterpart of the well known multivariate dimension-reduction-technique. A comprehensive overview of the existing methods is given, an estimation method based on the dual problem as well as the two-sample inference based on the functional principal component analysis are discussed. The FDA techniques are applied to the analysis of the implied volatility and yield curve dynamics. In addition, the implementation of the FDA techniques together with a FDA library for the statistical environment XploRe are presented.
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Wang, Wei. "Linear mixed effects models in functional data analysis." Thesis, University of British Columbia, 2008. http://hdl.handle.net/2429/253.
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Regression models with a scalar response and
a functional predictor have been extensively
studied. One approach is to approximate the
functional predictor using basis function or
eigenfunction expansions. In the expansion,
the coefficient vector can either be fixed or
random. The random coefficient vector
is also known as random effects and thus the
regression models are in a mixed effects
framework.
The random effects provide a model for the
within individual covariance of the
observations. But it also introduces an
additional parameter into the model, the
covariance matrix of the random effects.
This additional parameter complicates the
covariance matrix of the observations.
Possibly, the covariance parameters of the
model are not identifiable.
We study identifiability in normal linear
mixed effects models. We derive necessary and
sufficient conditions of identifiability,
particularly, conditions of identifiability
for the regression models with a scalar
response and a functional predictor using
random effects.
We study the regression model using the
eigenfunction expansion approach with random
effects. We assume the random effects have a
general covariance matrix
and the observed values of the predictor are
contaminated with measurement error.
We propose methods of inference for the
regression model's functional coefficient.
As an application of the model, we analyze a
biological data set to investigate the
dependence of a mouse's wheel running
distance on its body mass trajectory.
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Hu, Zonghui. "Semiparametric functional data analysis for longitudinal/clustered data: theory and application." Texas A&M University, 2004. http://hdl.handle.net/1969.1/3088.
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Semiparametric models play important roles in the field of biological statistics. In this dissertation, two types of semiparametic models are to be studied. One is the partially linear model, where the parametric part is a linear function. We are to investigate the two common estimation methods for the partially linear models when the data is correlated  longitudinal or clustered. The other is a semiparametric model where a latent covariate is incorporated in a mixed effects model. We will propose a semiparametric approach for estimation of this model and apply it to the study on colon carcinogenesis.
First, we study the profilekernel and backfitting methods in partially linear models for clustered/longitudinal data. For independent data, despite the potential rootn inconsistency of the backfitting estimator noted by Rice (1986), the two estimators have the same asymptotic variance matrix as shown by Opsomer and Ruppert (1999). In this work, theoretical comparisons of the two estimators for multivariate responses are investigated. We show that, for correlated data, backfitting often produces a larger asymptotic variance than the profilekernel method; that is, in addition to its bias problem, the backfitting estimator does not have the same asymptotic efficiency as the profilekernel estimator when data is correlated. Consequently, the common practice of using the backfitting method to compute profilekernel estimates is no longer advised. We illustrate this in detail by following Zeger and Diggle (1994), Lin and Carroll (2001) with a working independence covariance structure for nonparametric estimation and a correlated covariance structure for parametric estimation. Numerical performance of the two estimators is investigated through a simulation study. Their application to an ophthalmology dataset is also described.
Next, we study a mixed effects model where the main response and covariate variables are linked through the positions where they are measured. But for technical reasons, they are not measured at the same positions. We propose a semiparametric approach for this misaligned measurements problem and derive the asymptotic properties of the semiparametric estimators under reasonable conditions. An application of the semiparametric method to a colon carcinogenesis study is provided. We find that, as compared with the corn oil supplemented diet, fish oil supplemented diet tends to inhibit the increment of bcl2 (oncogene) gene expression in rats when the amount of DNA damage increases, and thus promotes apoptosis.
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Li, Yehua. "Topics in functional data analysis with biological applications." [College Station, Tex. : Texas A&M University, 2006. http://hdl.handle.net/1969.1/ETD-TAMU-1867.
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Jiang, Huijing. "Statistical computation and inference for functional data analysis." Diss., Georgia Institute of Technology, 2010. http://hdl.handle.net/1853/37087.
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My doctoral research dissertation focuses on two aspects of functional data analysis (FDA): FDA under spatial interdependence and FDA for multi-level data.
The first part of my thesis focuses on developing modeling and inference procedure for functional data under spatial dependence. The methodology introduced in this part is motivated by a research study on inequities in accessibility to financial services.
The first research problem in this part is concerned with a novel model-based method for clustering random time functions which are spatially interdependent. A cluster consists of time functions which are similar in shape. The time functions are decomposed into spatial global and time-dependent cluster effects using a semi-parametric model. We also assume that
the clustering membership is a realization from a Markov random field. Under these model assumptions, we borrow information across curves from nearby locations resulting in enhanced estimation accuracy of the cluster effects and of the cluster membership. In a simulation study, we assess the estimation accuracy of our clustering algorithm under a series of settings: small number of time points, high noise level and varying dependence structures. Over all simulation settings, the spatial-functional clustering method outperforms existing model-based clustering methods. In the case study presented in this project, we focus on estimates and classifies service accessibility patterns varying over a large geographic area (California and Georgia) and over a period of 15 years. The focus of this study is on financial services but it generally applies to any other service operation.
The second research project of this part studies an association analysis of space-time varying processes, which is rigorous, computational feasible and implementable with standard software. We introduce general measures to model different aspects of the temporal and spatial association between processes varying in space and time. Using a nonparametric spatiotemporal model, we show that the proposed association estimators are asymptotically unbiased and consistent. We complement the point association estimates with simultaneous confidence bands to assess the uncertainty in the point estimates. In a simulation study, we evaluate the accuracy of the association estimates with respect to the sample size as well as the coverage of the confidence bands. In the case study in this project, we investigate the association between service accessibility and income level. The primary objective of this association analysis is to assess whether there are significant changes in the income-driven equity of financial service accessibility over time and to identify potential under-served markets.
The second part of the thesis discusses novel statistical methodology for analyzing multilevel functional data including a clustering method based on a functional ANOVA model and a spatio-temporal model for functional data with a nested hierarchical structure. In this part, I introduce and compare a series of clustering approaches for multilevel functional data. For brevity, I present the clustering methods for two-level data: multiple samples of random functions, each sample corresponding to a case and each random function within a sample/case corresponding to a measurement type. A cluster consists of cases which have similar within-case means (level-1 clustering) or similar between-case means (level-2 clustering). Our primary focus is to evaluate a model-based clustering to more straightforward hard clustering methods. The clustering model is based on a multilevel functional principal component analysis. In a simulation study, we assess the estimation accuracy of our clustering algorithm under a series of settings: small vs. moderate number of time points, high noise level and small number of measurement types. We demonstrate the applicability of the clustering analysis to a real data set consisting of time-varying sales for multiple products sold by a large retailer in the U.S.
My ongoing research work in multilevel functional data analysis is developing a statistical model for estimating temporal and spatial associations of a series of time-varying variables with an intrinsic nested hierarchical structure. This work has a great potential in many real applications where the data are areal data collected from different data sources and over geographic regions of different spatial resolution.
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Wagner, Heiko [Verfasser]. "A Contribution to Functional Data Analysis / Heiko Wagner." Bonn : Universitäts- und Landesbibliothek Bonn, 2016. http://d-nb.info/1122193726/34.
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Rubanova, Natalia. "MasterPATH : network analysis of functional genomics screening data." Thesis, Sorbonne Paris Cité, 2018. http://www.theses.fr/2018USPCC109/document.
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Dans ce travail nous avons élaboré une nouvelle méthode de l'analyse de réseau à définir des membres possibles des voies moléculaires qui sont important pour ce phénotype en utilisant la « hit-liste » des expériences « omics » qui travaille dans le réseau intégré (le réseau comprend des interactions protéine-protéine, de transcription, l’acide ribonucléique micro-l’acide ribonucléique messager et celles métaboliques). La méthode tire des sous-réseaux qui sont construit des voies de quatre types les plus courtes (qui ne se composent des interactions protéine-protéine, ayant au minimum une interaction de transcription, ayant au minimum une interaction l’acide ribonucléique micro-l’acide ribonucléique messager, ayant au minimum une interaction métabolique) entre des hit –gènes et des soi-disant « exécuteurs terminaux » - les composants biologiques qui participent à la réalisation du phénotype finale (s’ils sont connus) ou entre les hit-gènes (si « des exécuteurs terminaux » sont inconnus). La méthode calcule la valeur de la centralité de chaque point culminant et de chaque voie dans le sous-réseau comme la quantité des voies les plus courtes trouvées sur la route précédente et passant à travers le point culminant et la voie. L'importance statistique des valeurs de la centralité est estimée en comparaison avec des valeurs de la centralité dans les sous-réseaux construit des voies les plus courtes pour les hit-listes choisi occasionnellement. Il est supposé que les points culminant et les voies avec les valeurs de la centralité statistiquement signifiantes peuvent être examinés comme les membres possibles des voies moléculaires menant à ce phénotype. S’il y a des valeurs expérimentales et la P-valeur pour un grand nombre des points culminant dans le réseau, la méthode fait possible de calculer les valeurs expérimentales pour les voies (comme le moyen des valeurs expérimentales des points culminant sur la route) et les P-valeurs expérimentales (en utilisant la méthode de Fischer et des transpositions multiples).A l'aide de la méthode masterPATH on a analysé les données de la perte de fonction criblage de l’acide ribonucléique micro et l'analyse de transcription de la différenciation terminal musculaire et les données de la perte de fonction criblage du procès de la réparation de l'ADN. On peut trouver le code initial de la méthode si l’on suit le lien https://github.com/daggoo/masterPATHIn this work we developed a new exploratory network analysis method, that works on an integrated network (the network consists of protein-protein, transcriptional, miRNA-mRNA, metabolic interactions) and aims at uncovering potential members of molecular pathways important for a given phenotype using hit list dataset from “omics” experiments. The method extracts subnetwork built from the shortest paths of 4 different types (with only protein-protein interactions, with at least one transcription interaction, with at least one miRNA-mRNA interaction, with at least one metabolic interaction) between hit genes and so called “final implementers” – biological components that are involved in molecular events responsible for final phenotypical realization (if known) or between hit genes (if “final implementers” are not known). The method calculates centrality score for each node and each path in the subnetwork as a number of the shortest paths found in the previous step that pass through the node and the path. Then, the statistical significance of each centrality score is assessed by comparing it with centrality scores in subnetworks built from the shortest paths for randomly sampled hit lists. It is hypothesized that the nodes and the paths with statistically significant centrality score can be considered as putative members of molecular pathways leading to the studied phenotype. In case experimental scores and p-values are available for a large number of nodes in the network, the method can also calculate paths’ experiment-based scores (as an average of the experimental scores of the nodes in the path) and experiment-based p-values (by aggregating p-values of the nodes in the path using Fisher’s combined probability test and permutation approach). The method is illustrated by analyzing the results of miRNA loss-of-function screening and transcriptomic profiling of terminal muscle differentiation and of ‘druggable’ loss-of-function screening of the DNA repair process. The Java source code is available on GitHub page https://github.com/daggoo/masterPATH
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Arisido, Maeregu Woldeyes. "Functional Data Analysis for Environmental Pollutants and Health." Doctoral thesis, Università degli studi di Padova, 2015. http://hdl.handle.net/11577/3424647.
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The adverse health effect of exposure to high pollutant concentration has been the focus of many recent studies. This is particularly true for ground level ozone which is considered in the present thesis. The effect has been estimated at different geographic locations, and it has been shown that it may be spatially heterogeneous. Within such widely accepted studies, two major issues arise which are the focus of this thesis: how to best measure daily individual exposure to a pollutant and how the health effect of the exposure is affected by geographic location both in strength and shape. The first issue is related to the fact that the concentration of ozone varies widely during the day, producing a distinctive daily pattern. Traditionally, the daily pattern of the pollutant is collapsed to a single summary figure which is then taken to represent daily individual exposure. In this thesis, we propose a more accurate approaches to measure pollutant exposure which address the limitations in the use of the standard exposure measure. The methods are based on principle of functional data analysis, which treats the daily pattern of concentration as a function to account for temporal variation of the pollutant. The predictive efficiency of our approach is superior to that of models based on the standard exposure measures. We propose a functional hierarchical approach to model data which are coming from multiple geographic locations, and estimate pollutant exposure effect allowing daily variation and spatial heterogeneity of the effect at once. The approach is general and can also be considered as the analogue of the multilevel models to the case in which the predictor is functional and the response is scalar.Numerosi studi recenti hanno mostrato l'effetto dannoso che l'esposizione a elevate concentrazioni di inquinanti ha sulla salute umana. In particolare, questo avviene per l'ozono, del quale ci occupiamo nel presente lavoro. Stime ottenute in diversi siti mostrano che l'effetto è geograficamente eterogeneo. Nel contesto degli studi menzionati emergono due aspetti di particolare importanza, e su cui è incentrato il presente lavoro: come misurare al meglio l'esposizione individuale e come e in che misura l'effetto vari geograficamente, sia quanto a intensità che a forma. La prima questione è legata al fatto che la concentrazione di ozono mostra ampie variazioni nel corso di una giornata. Di tale andamento giornaliero non si tiene conto nella maggior parte degli studi epidemiologici, e si assume che possa essere efficacemente riassunto da una statistica unidimensionale. Nel presente lavoro proponiamo degli approcci che si basano sull'impiego di misure della concentrazione che tengono conto dell'andamento temporale della stessa. Tali approcci sono basati sulla metodologia dell'analisi dei dati funzionali, che consiste nel trattare il dato sulla concentrazione giornaliera come una funzione, tenendo così conto delle sue variazioni durante la giornata. In termini previsivi, si è verificato che tale approccio porta a un miglioramento rispetto ai modelli basati su una statistica giornaliera. Questo approccio è poi esteso al caso di dati multisito, per i quali si propone un modello funzionale gerarchico, che consentono di stimare l'effetto dell'esposizione all'inquinante tenendo conto da un lato della variazione giornaliera della concentrazione dello stesso e dell'eterogeneità nello spazio di tale effetto. Questo approccio può essere visto come l'analogo di un modello multilivello per il caso in cui il predittore è funzionale e la variabile risposta scalare.
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Zhang, Wen 1978. "Functional data analysis for detecting structural boundaries of cortical area." Thesis, McGill University, 2005. http://digitool.Library.McGill.CA:80/R/?func=dbin-jump-full&object_id=98531.
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It is widely accepted that the cortex can be divided into a series of spatially discrete areas based on their specific laminar patterns. It is of great interest to divide the cortex into different areas in terms of both neuronal functions and cellular composition. The division of cortical areas can be reflected by the cell arrangements or cellular composition. Therefore, the cortical structure can be represented by some functional neuronal density data. Techniques on functional data analysis help to develop some measures which indicate structural changes.In order to separate roughness from structural variations and influences of the convolutions and foldings, a method called bivariate smoothing is proposed for the noisy density data. This smoothing method is applied to four sets of cortical density data provided by Prof Petrides [1] and Scott Mackey [2].
The first or second order derivatives of the density function reflect the change and the rate of the change of the density, respectively. Therefore, derivatives of the density function are applied to analyze the structural features as an attempt to detect indicators for boundaries of subareas of the four cortex sections.
Finally, the accuracy and limitation of this smoothing method is tested using some simulated examples.
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Charles, Nathan Richard. "Data model refinement, generic profiling, and functional programming." Thesis, University of York, 2001. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.341629.
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Sheppard, Therese. "Extending covariance structure analysis for multivariate and functional data." Thesis, University of Manchester, 2010. https://www.research.manchester.ac.uk/portal/en/theses/extending-covariance-structure-analysis-for-multivariate-and-functional-data(e2ad7f12-3783-48cf-b83c-0ca26ef77633).html.
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For multivariate data, when testing homogeneity of covariance matrices arising from two or more groups, Bartlett's (1937) modified likelihood ratio test statistic is appropriate to use under the null hypothesis of equal covariance matrices where the null distribution of the test statistic is based on the restrictive assumption of normality. Zhang and Boos (1992) provide a pooled bootstrap approach when the data cannot be assumed to be normally distributed. We give three alternative bootstrap techniques to testing homogeneity of covariance matrices when it is both inappropriate to pool the data into one single population as in the pooled bootstrap procedure and when the data are not normally distributed. We further show that our alternative bootstrap methodology can be extended to testing Flury's (1988) hierarchy of covariance structure models. Where deviations from normality exist, we show, by simulation, that the normal theory log-likelihood ratio test statistic is less viable compared with our bootstrap methodology. For functional data, Ramsay and Silverman (2005) and Lee et al (2002) together provide four computational techniques for functional principal component analysis (PCA) followed by covariance structure estimation. When the smoothing method for smoothing individual profiles is based on using least squares cubic B-splines or regression splines, we find that the ensuing covariance matrix estimate suffers from loss of dimensionality. We show that ridge regression can be used to resolve this problem, but only for the discretisation and numerical quadrature approaches to estimation, and that choice of a suitable ridge parameter is not arbitrary. We further show the unsuitability of regression splines when deciding on the optimal degree of smoothing to apply to individual profiles. To gain insight into smoothing parameter choice for functional data, we compare kernel and spline approaches to smoothing individual profiles in a nonparametric regression context. Our simulation results justify a kernel approach using a new criterion based on predicted squared error. We also show by simulation that, when taking account of correlation, a kernel approach using a generalized cross validatory type criterion performs well. These data-based methods for selecting the smoothing parameter are illustrated prior to a functional PCA on a real data set.
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Vogetseder, Georg. "Functional Analysis of Real World Truck Fuel Consumption Data." Thesis, Halmstad University, School of Information Science, Computer and Electrical Engineering (IDE), 2008. http://urn.kb.se/resolve?urn=urn:nbn:se:hh:diva-1148.
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This thesis covers the analysis of sparse and irregular fuel consumption data of long
distance haulage articulate trucks. It is shown that this kind of data is hard to analyse with multivariate as well as with functional methods. To be able to analyse the data, Principal Components Analysis through Conditional Expectation (PACE) is used, which enables the use of observations from many trucks to compensate for the sparsity of observations in order to get continuous results. The principal component scores generated by PACE, can then be used to get rough estimates of the trajectories for single trucks as well as to detect outliers. The data centric approach of PACE is very useful to enable functional analysis of sparse and irregular data. Functional analysis is desirable for this data to sidestep feature extraction and enabling a more natural view on the data.
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Paszkowski-Rogacz, Maciej. "Integration and analysis of phenotypic data from functional screens." Doctoral thesis, Saechsische Landesbibliothek- Staats- und Universitaetsbibliothek Dresden, 2011. http://nbn-resolving.de/urn:nbn:de:bsz:14-qucosa-63063.
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Motivation: Although various high-throughput technologies provide a lot of valuable information, each of them is giving an insight into different aspects of cellular activity and each has its own limitations. Thus, a complete and systematic understanding of the cellular machinery can be achieved only by a combined analysis of results coming from different approaches. However, methods and tools for integration and analysis of heterogenous biological data still have to be developed.
Results: This work presents systemic analysis of basic cellular processes, i.e. cell viability and cell cycle, as well as embryonic stem cell pluripotency and differentiation. These phenomena were studied using several high-throughput technologies, whose combined results were analysed with existing and novel clustering and hit selection algorithms.
This thesis also introduces two novel data management and data analysis tools. The first, called DSViewer, is a database application designed for integrating and querying results coming from various genome-wide experiments. The second, named PhenoFam, is an application performing gene set enrichment analysis by employing structural and functional information on families of protein domains as annotation terms. Both programs are accessible through a web interface.
Conclusions: Eventually, investigations presented in this work provide the research community with novel and markedly improved repertoire of computational tools and methods that facilitate the systematic analysis of accumulated information obtained from high-throughput studies into novel biological insights.
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Cheng, Yafeng. "Functional regression analysis and variable selection for motion data." Thesis, University of Newcastle upon Tyne, 2016. http://hdl.handle.net/10443/3150.
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Modern technology o ers us highly evolved data collection devices. They allow us to observe data densely over continua such as time, distance, space and so on. The observations are normally assumed to follow certain continuous and smooth underline functions of the continua. Thus the analysis must consider two important properties of functional data: infinite dimension and the smoothness. Traditional multivariate data analysis normally works with low dimension and independent data. Therefore, we need to develop new methodology to conduct functional data analysis. In this thesis, we first study the linear relationship between a scalar variable and a group of functional variables using three di erent discrete methods. We combine this linear relationship with the idea from least angle regression to propose a new variable selection method, named as functional LARS. It is designed for functional linear regression with scalar response and a group of mixture of functional and scalar variables. We also propose two new stopping rules for the algorithm, since the conventional stopping rules may fail for functional data. The algorithm can be used when there are more variables than samples. The performance of the algorithm and the stopping rules is compared with existed algorithms by comprehensive simulation studies. The proposed algorithm is applied to analyse motion data including scalar response, more than 200 scalar covariates and 500 functional covariates. Models with or without functional variables are compared. We have achieved very accurate results for this complex data particularly the models including functional covariates. The research in functional variable selection is limited due to its complexity and onerous computational burdens. We have demonstrated that the proposed functional LARS is a very e cient method and can cope with functional data very large dimension. The methodology and the idea have the potential to be used to address other challenging problems in functional data analysis.
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Wang, Shanshan. "Exploring and modeling online auctions using functional data analysis." College Park, Md. : University of Maryland, 2007. http://hdl.handle.net/1903/6962.
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Thesis (Ph. D.) -- University of Maryland, College Park, 2007.Thesis research directed by: Mathematics. Title from t.p. of PDF. Includes bibliographical references. Published by UMI Dissertation Services, Ann Arbor, Mich. Also available in paper.
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Liu, Haiyan [Verfasser]. "On Functional Data Analysis with Dependent Errors / Haiyan Liu." Konstanz : Bibliothek der Universität Konstanz, 2016. http://d-nb.info/1114894222/34.
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Doehring, Orlando. "Peak selection in metabolic profiles using functional data analysis." Thesis, Imperial College London, 2013. http://hdl.handle.net/10044/1/11062.
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In this thesis we describe sparse principal component analysis (PCA) methods and apply them to the analysis of short multivariate time series in order to perform both dimensionality reduction and variable selection. We take a functional data analysis (FDA) modelling approach in which each time series is treated as a continuous smooth function of time or curve. These techniques have been applied to analyse time series data arising in the area of metabonomics. Metabonomics studies chemical processes involving small molecule metabolites in a cell. We use experimental data obtained from the COnsortium for MEtabonomic Toxicology (COMET) project which is formed by six pharmaceutical companies and Imperial College London, UK. In the COMET project repeated measurements of several metabolites over time were collected which are taken from rats subjected to different drug treatments. The aim of our study is to detect important metabolites by analysing the multivariate time series. Multivariate functional PCA is an exploratory technique to describe the observed time series. In its standard form, PCA involves linear combinations of all variables (i.e. metabolite peaks) and does not perform variable selection. In order to select a subset of important metabolites we introduce sparsity into the model. We develop a novel functional Sparse Grouped Principal Component Analysis (SGPCA) algorithm using ideas related to Least Absolute Shrinkage and Selection Operator (LASSO), a regularized regression technique, with grouped variables. This SGPCA algorithm detects a sparse linear combination of metabolites which explain a large proportion of the variance. Apart from SGPCA, we also propose two alternative approaches for metabolite selection. The first one is based on thresholding the multivariate functional PCA solution, while the second method computes the variance of each metabolite curve independently and then proceeds to these rank curves in decreasing order of importance. To the best of our knowledge, this is the first application of sparse functional PCA methods to the problem of modelling multivariate metabonomic time series data and selecting a subset of metabolite peaks. We present comprehensive experimental results using simulated data and COMET project data for different multivariate and functional PCA variants from the literature and for SGPCA . Simulation results show that that the SGPCA algorithm recovers a high proportion of truly important metabolite variables. Furthermore, in the case of SGPCA applied to the COMET dataset we identify a small number of important metabolites independently for two different treatment conditions. A comparison of selected metabolites in both treatment conditions reveals that there is an overlap of over 75 percent.
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Zhang, Bairu. "Functional data analysis in orthogonal designs with applications to gait patterns." Thesis, Queen Mary, University of London, 2018. http://qmro.qmul.ac.uk/xmlui/handle/123456789/44698.
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This thesis presents a contribution to the active research area of functional data analysis (FDA) and is concerned with the analysis of data from complex experimental designs in which the responses are curves. High resolution, closely correlated data sets are encountered in many research fields, but current statistical methodologies often analyse simplistic summary measures and therefore limit the completeness and accuracy of conclusions drawn. Specifically the nature of the curves and experimental design are not taken into account. Mathematically, such curves can be modelled either as sample paths of a stochastic process or as random elements in a Hilbert space. Despite this more complex type of response, the structure of experiments which yield functional data is often the same as in classical experimentation. Thus, classical experimental design principles and results can be adapted to the FDA setting. More specifically, we are interested in the functional analysis of variance (ANOVA) of experiments which use orthogonal designs. Most of the existing functional ANOVA approaches consider only completely randomised designs. However, we are interested in more complex experimental arrangements such as, for example, split-plot and row-column designs. Similar to univariate responses, such complex designs imply that the response curves for different observational units are correlated. We use the design to derive a functional mixed-effects model and adapt the classical projection approach in order to derive the functional ANOVA. As a main result, we derive new functional F tests for hypotheses about treatment effects in the appropriate strata of the design. The approximate null distribution of these tests is derived by applying the Karhunen- Lo`eve expansion to the covariance functions in the relevant strata. These results extend existing work on functional F tests for completely randomised designs. The methodology developed in the thesis has wide applicability. In particular, we consider novel applications of functional F tests to gait analysis. Results are presented for two empirical studies. In the first study, gait data of patients with cerebral palsy were collected during barefoot walking and walking with ankle-foot orthoses. The effects of ankle-foot orthoses are assessed by functional F tests and compared with pointwise F tests and the traditional univariate repeated-measurements ANOVA. The second study is a designed experiment in which a split-plot design was used to collect gait data from healthy subjects. This is commonly done in gait research in order to better understand, for example, the effects of orthoses while avoiding confounded analysis from the high variability observed in abnormal gait. Moreover, from a technical point of view the study may be regarded as a real-world alternative to simulation studies. By using healthy individuals it is possible to collect data which are in better agreement with the underlying model assumptions. The penultimate chapter of the thesis presents a qualitative study with clinical experts to investigate the utility of gait analysis for the management of cerebral palsy. We explore potential pathways by which the statistical analyses in the thesis might influence patient outcomes. The thesis has six chapters. After describing motivation and introduction in Chapter 1, mathematical representations of functional data are presented in Chapter 2. Chapter 3 considers orthogonal designs in the context of functional data analysis. New functional F tests for complex designs are derived in Chapter 4 and applied in two gait studies. Chapter 5 is devoted to a qualitative study. The thesis concludes with a discussion which details the extent to which the research question has been addressed, the limitations of the work and the degree to which it has been answered.
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Fitzgerald-DeHoog, Lindsay M. "Multivariate analysis of proteomic data| Functional group analysis using a global test." Thesis, California State University, Long Beach, 2015. http://pqdtopen.proquest.com/#viewpdf?dispub=1602759.
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Proteomics is a relatively new discipline being implemented in life science fields. Proteomics allows a whole-systems approach to discerning changes in organismal physiology due to physical perturbations. The advantages of a proteomic approach may be counteracted by the ability to analyze the data in a meaningful way due to inherent problems with statistical assumptions. Furthermore, analyzing significant protein volume differences among treatment groups often requires analysis of numerous proteins even when limiting analyses to a particular protein type or physiological pathway. Improper use of traditional techniques leads to problems with multiple hypotheses testing.
This research will examine two common techniques used to analyze proteomic data and will apply these to a novel proteomic data set. In addition, a Global Test originally developed for gene array data will be employed to discover its utility for proteomic data and the ability to counteract the multiple hypotheses testing problems encountered with traditional analyses.
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Burrell, Lauren S. "Feature analysis of functional mri data for mapping epileptic networks." Diss., Georgia Institute of Technology, 2008. http://hdl.handle.net/1853/26528.
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This research focused on the development of a methodology for analyzing functional magnetic resonance imaging (fMRI) data collected from patients with epilepsy in order to map epileptic networks. Epilepsy, a chronic neurological disorder characterized by recurrent, unprovoked seizures, affects up to 1% of the world's population. Antiepileptic drug therapies either do not successfully control seizures or have unacceptable side effects in over 30% of patients. Approximately one-third of patients whose seizures cannot be controlled by medication are candidates for surgical removal of the affected area of the brain, potentially rendering them seizure free. Accurate localization of the epileptogenic focus, i.e., the area of seizure onset, is critical for the best surgical outcome. The main objective of the research was to develop a set of fMRI data features that could be used to distinguish between normal brain tissue and the epileptic focus. To determine the best combination of features from various domains for mapping the focus, genetic programming and several feature selection methods were employed. These composite features and feature sets were subsequently used to train a classifier capable of discriminating between the two classes of voxels. The classifier was then applied to a separate testing set in order to generate maps showing brain voxels labeled as either normal or epileptogenic based on the best feature or set of features. It should be noted that although this work focuses on the application of fMRI analysis to epilepsy data, similar techniques could be used when studying brain activations due to other sources. In addition to investigating in vivo data collected from temporal lobe epilepsy patients with uncertain epileptic foci, phantom (simulated) data were created and processed to provide quantitative measures of the efficacy of the techniques.
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McGonigle, John. "Data-driven analysis methods in pharmacological and functional magnetic resonance." Thesis, University of Bristol, 2012. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.573929.
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This thesis introduces several novel methods for the data-driven and ex- ploratory analysis of functional brain images. Functional magnetic resonance imaging (fMRI) has emerged as a safe and non-invasive way to image the hu- man brain in action. In pharmacological MRI (phMRI), a drug's effect on the brain is of interest, rather than the brain's response to a specific task as in fMRI. However, the sometimes prolonged response to a drug necessi- tates different methodologies than those for task related effects, with further methods development needed to deliver robust results so that phMRI may be of practical use during drug development. There are many confounding issues in analysing these data, including under-informed models of response, subject motion, scanner drift, and gross differences in brain volume. In this work, data from a phMRI experiment was analysed to examine the effect of a pharmacological dose of hydrocortisone; a glucocorticoid associ- ated with the body's response to stress, and used in a number of medical conditions. The key findings were that even without using a priori hypothe- ses about the site of action, hydrocortisone significantly reduces a phMRI signal associated with blood oxygenation in the dorsal hippocampi, which is confirmed by decreases in absolute perfusion measured using arterial spin labelling. Methods were developed for the detection and correction of artefacts, includ- ing intra-scan motion and scanner drift. Functional connectivity methods were examined, and methodological issues in comparing groups investigated, revealing that many previously observed differences may have been biased or even artefactual due to gross differences in brain volume. Temporal decom- position techniques were also explored for their use in brain imaging, with wavelet cluster analysis being developed into an interactive and iterative method, while an adaptive analysis method, empirical mode decomposition, is built upon to allow the analysis of many thousands of time courses.
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Lee, Homin, William Braynen, Kiran Keshav, and Paul Pavlidis. "ErmineJ: Tool for functional analysis of gene expression data sets." BioMed Central, 2005. http://hdl.handle.net/10150/610121.
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BACKGROUND:It is common for the results of a microarray study to be analyzed in the context of biologically-motivated groups of genes such as pathways or Gene Ontology categories. The most common method for such analysis uses the hypergeometric distribution (or a related technique) to look for "over-representation" of groups among genes selected as being differentially expressed or otherwise of interest based on a gene-by-gene analysis. However, this method suffers from some limitations, and biologist-friendly tools that implement alternatives have not been reported.RESULTS:We introduce ErmineJ, a multiplatform user-friendly stand-alone software tool for the analysis of functionally-relevant sets of genes in the context of microarray gene expression data. ErmineJ implements multiple algorithms for gene set analysis, including over-representation and resampling-based methods that focus on gene scores or correlation of gene expression profiles. In addition to a graphical user interface, ErmineJ has a command line interface and an application programming interface that can be used to automate analyses. The graphical user interface includes tools for creating and modifying gene sets, visualizing the Gene Ontology as a table or tree, and visualizing gene expression data. ErmineJ comes with a complete user manual, and is open-source software licensed under the Gnu Public License.CONCLUSION:The availability of multiple analysis algorithms, together with a rich feature set and simple graphical interface, should make ErmineJ a useful addition to the biologist's informatics toolbox. ErmineJ is available from http://microarray.cu.genome.org webcite.
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Chen, Jinsong. "Variance analysis for kernel smoothing of a varying-coefficient model with longitudinal data /." Electronic version (PDF), 2003. http://dl.uncw.edu/etd/2003/chenj/jinsongchen.pdf.
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Pokhrel, Keshav Prasad. "Statistical Analysis and Modeling of Brain Tumor Data: Histology and Regional Effects." Scholar Commons, 2013. http://scholarcommons.usf.edu/etd/4746.
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Comprehensive statistical models for non-normally distributed cancerous tumor sizes are
of prime importance in epidemiological studies, whereas a long term forecasting models
can facilitate in reducing complications and uncertainties of medical progress. The statistical
forecasting models are critical for a better understanding of the disease and supply
appropriate treatments. In addition such a model can be used for the allocations of budgets,
planning, control and evaluations of ongoing efforts of prevention and early detection of
the diseases.
In the present study, we investigate the effects of age, demography, and race on primary
brain tumor sizes using quantile regression methods to obtain a better understanding of the
malignant brain tumor sizes. The study reveals that the effects of risk factors together with
the probability distributions of the malignant brain tumor sizes, and plays significant role in
understanding the rate of change of tumor sizes. The data that our analysis and modeling is
based on was obtained from Surveillance Epidemiology and End Results (SEER) program
of the United States.
We also analyze the discretely observed brain cancer mortality rates using functional
data analysis models, a novel approach in modeling time series data, to obtain more accurate
and relevant forecast of the mortality rates for the US. We relate the cancer registries,
race, age, and gender to age-adjusted brain cancer mortality rates and compare the variations
of these rates during the period of the study that data was collected.
Finally, in the present study we have developed effective statistical model for heterogenous
and high dimensional data that forecast the hazard rates with high degree of accuracy,
that will be very helpful to address subject health problems at present and in the future.
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Jin, Zhongnan. "Statistical Methods for Multivariate Functional Data Clustering, Recurrent Event Prediction, and Accelerated Degradation Data Analysis." Diss., Virginia Tech, 2019. http://hdl.handle.net/10919/102628.
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In this dissertation, we introduce three projects in machine learning and reliability applications after the general introductions in Chapter 1. The first project concentrates on the multivariate sensory data, the second project is related to the bivariate recurrent process, and the third project introduces thermal index (TI) estimation in accelerated destructive degradation test (ADDT) data, in which an R package is developed. All three projects are related to and can be used to solve certain reliability problems. Specifically, in Chapter 2, we introduce a clustering method for multivariate functional data. In order to cluster the customized events extracted from multivariate functional data, we apply the functional principal component analysis (FPCA), and use a model based clustering method on a transformed matrix. A penalty term is imposed on the likelihood so that variable selection is performed automatically.
In Chapter 3, we propose a covariate-adjusted model to predict next event in a bivariate recurrent event system. Inspired by geyser eruptions in Yellowstone National Park, we consider two event types and model their event gap time relationship. External systematic conditions are taken account into the model with covariates. The proposed covariate adjusted recurrent process (CARP) model is applied to the Yellowstone National Park geyser data.
In Chapter 4, we compare estimation methods for TI. In ADDT, TI is an important index indicating the reliability of materials, when the accelerating variable is temperature. Three methods are introduced in TI estimations, which are least-squares method, parametric model and semi-parametric model. An R package is implemented for all three methods. Applications of R functions are introduced in Chapter 5 with publicly available ADDT datasets.
Chapter 6 includes conclusions and areas for future works.Doctor of Philosophy
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MacKelvie, Erin. "A Comparison of Traditional Aggregated Data to a Comprehensive Second-by-Second Data Depiction in Functional Analysis Graphs." Scholarly Commons, 2021. https://scholarlycommons.pacific.edu/uop_etds/3730.
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Functional analyses (FAs) are an important component of treatment and the data gathered from FAs are often graphed in an aggregate or summary format, such as mean rate per session. Given the prevalence of undifferentiated analyses, it may be that this common method of data depiction is incomplete. In this paper, we compare the traditional aggregate method to a comprehensive second-by-second demonstration of the data including all appropriate and inappropriate responses emitted, as well as programmed and accidental antecedent and consequent variables, which may help further clarify the results of a functional analysis. We compared the functional analysis results of two participants when the data were depicted using the traditional rate aggregate method and depicted using a comprehensive second-by-second method. Although both rate and comprehensive second-by-second data depiction resulted in similar conclusions regarding the maintaining variables for the participants, comprehensive second-by-second data depiction allowed us to draw the conclusions in less time. Additional advantages and disadvantages of each method as it relates to efficiency, therapeutic risk and safety, and practicality are also discussed. Keywords: efficiency, functional analysis, problem behavior, safety, within-session second-by-second analysis.
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Jiang, Cheng. "Investigation and application of functional data analysis technology for calibration of near-infrared spectroscopic data." Thesis, University of Newcastle Upon Tyne, 2009. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.601687.
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This thesis focuses on the investigation and application of functional Data Analysis methodologies to address calibration challenges of spectroscopic data. Of particular interest is the area of calibration of near-infrared spectral data. Different strategies to construct functional linear calibration methodologies and a number of functional linear calibration approaches are initially discussed. A novel approach is then proposed to compare functional linear calibration methodologies with a well established and widely used methodology in the chemometrics area, Partial Least Squares (PLS). From this perspective, a common framework can be established to investigate the similarities and differences between these two methodologies. It is shown that the model structures of these two methodologies are similar but the difference is the selection of basis function to represent the original spectral data. As opposed to the loadings of PLS, B-splines capture local features of the data.
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Zhou, Rensheng. "Degradation modeling and monitoring of engineering systems using functional data analysis." Diss., Georgia Institute of Technology, 2012. http://hdl.handle.net/1853/45897.
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In this thesis, we develop several novel degradation models based on techniques from functional data analysis. These models are suitable for characterizing different types of sensor-based degradation signals, whether they are censored at a certain fixed time point or truncated at the failure threshold. Our proposed models can also be easily extended to accommodate for the effects of environmental conditions on degradation processes. Unlike many existing degradation models that rely on the existence of a historical sample of complete degradation signals, our modeling framework is well-suited for modeling complete as well as incomplete (sparse and fragmented) degradation signals. We utilize these models to predict and continuously update, in real time, the residual life distributions of partially degraded components. We assess and compare the performance of our proposed models and existing benchmark models by using simulated signals and real world data sets. The results indicate that our models can provide a better characterization of the degradation signals and a more accurate prediction of a system's lifetime under different signal scenarios. Another major advantage of our models is their robustness to the model mis-specification, which is especially important for applications with incomplete degradation signals (sparse or fragmented).
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Gabrys, Robertas. "Goodness-of-Fit and Change-Point Tests for Functional Data." DigitalCommons@USU, 2010. https://digitalcommons.usu.edu/etd/658.
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A test for independence and identical distribution of functional observations is proposed in this thesis. To reduce dimension, curves are projected on the most important functional principal components. Then a test statistic based on lagged cross--covariances of the resulting vectors is constructed. We show that this dimension reduction step introduces asymptotically negligible terms, i.e. the projections behave asymptotically as iid vector--valued observations. A complete asymptotic theory based on correlations of random matrices, functional principal component expansions, and Hilbert space techniques is developed. The test statistic has chi-square asymptotic null distribution.
Two inferential tests for error correlation in the functional linear model are put forward. To construct them, finite dimensional residuals are computed in two different ways, and then their autocorrelations are suitably defined. From these autocorrelation matrices, two quadratic forms are constructed whose limiting distributions are chi--squared with known numbers of degrees of freedom (different for the two forms).
A test for detecting a change point in the mean of functional observations is developed. The null distribution of the test statistic is asymptotically pivotal with a well-known asymptotic distribution. A comprehensive asymptotic theory for the estimation of a change--point in the mean function of functional observations is developed.
The procedures developed in this thesis can be readily computed using the R package fda. All theoretical insights obtained in this thesis are confirmed by simulations and illustrated by real life-data examples.
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Ferguson, Alexander B. "Higher order strictness analysis by abstract interpretation over finite domains." Thesis, University of Glasgow, 1995. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.308143.
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Battey, Heather Suzanne. "Dimension reduction and automatic smoothing in high dimensional and functional data analysis." Thesis, University of Cambridge, 2011. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.609849.
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Dierickx, Lawrence O. "Quantitative data analysis and functional testicular evaluation using PET-CT and FDG." Thesis, Toulouse 3, 2016. http://www.theses.fr/2016TOU30400.
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Le but de cette thèse est d'évaluer l'utilisation de la TEP/CT avec le 18F-FDG pour l'évaluation de la fonction testiculaire et d'optimiser et de standardiser le protocole d'acquisition et l'analyse du volume testiculaire pour ce faire. Dans le chapitre I, nous donnons un aperçu de la littérature où nous établissons que l'absorption de 18F-FDG est corrélée avec la spermatogenèse en raison de la présence des transporteurs GLUT 3 sur les cellules de Sertoli et les spermatides et non sur les cellules de Leydig qui sont responsables de la stéroïdogenèse. Nous donnons ensuite un aperçu du problème de santé publique que pose la stérilité masculine en indiquant les différentes applications cliniques possibles de l'imagerie fonctionnelle des testicules. Dans le chapitre II, nous examinons la corrélation significative entre l'absorption de 18F-FDG en termes d'intensité et de volume d'absorption et la fonction testiculaire via les paramètres de l'analyse du sperme. Dans le chapitre III, nous nous concentrons sur la standardisation du protocole d'acquisition pour cette indication spécifique, après un bref aperçu technique de la TEP/TDM et de ses limites. La première étude ayant été réalisée par le biais d'un volume testiculaire délimité manuellement, nous avons ré-analysé la corrélation avec une méthode de segmentation adaptative solide et reproductible du volume dans un deuxième article. Nous nous sommes également concentrés sur l'optimisation du protocole d'acquisition en évaluant l'impact de l'activité urinaire intense sur l'absorption testiculaire. Nous avons d'abord examiné cet impact à l'aide d'études de fantômes dans lesquelles nous avons simulé la vessie et les testicules. Nous avons ensuite procédé à une étude clinique visant à évaluer et à comparer deux protocoles de diurétiques. Dans le chapitre IV, nous abordons le sujet important, et encore plus dans ce contexte andrologique, des problèmes liés à la radioprotection d'une TEP/CT avec le 18F-FDG. Enfin, dans le chapitre V, nous donnons un aperçu de certaines des questions qui restent à traiter et des perspectives futures de cette nouvelle orientation dans le domaine de la médecine nucléaire que nous pourrions appeler "andrologie nucléaire"The aim of this thesis is to evaluate the use of PET/CT with 18F-FDG for an assessment of the testicular function and to optimise and standardise the acquisition protocol and the testicular volume analysis in order to do that. In chapter I we provide a literature overview where we establish that the 18F-FDG uptake is correlated with the spermatogenesis because of the presence of GLUT 3 transporters on the Sertoli cells and the spermatides and not on the Leydig cells which are responsible for the steroidogenesis. We then provide an overview of the public health problem of male infertility where we point out different possible clinical applications for testicular functional imaging. In chapter II we examine the significant correlation between 18F-FDG uptake in terms of intensity and volume of uptake and the testicular function via the parameters of the sperm analysis. In chapter III, we focus on the standardisation of the acquisition protocol for this specific indication, after a brief technical overview of the PET/CT and of its limitations. Because the first study was done via a manually delineated testicular volume, we re-analysed the correlation with a solid and reproducible adaptive volume segmentation method in a second article. We further focussed on optimising the acquisition protocol by evaluating the impact of the intense urinary activity on the testicular uptake. First we examined this impact with phantom studies where we simulated the bladder and the testes. We proceeded with a clinical study where we aimed to evaluate and compare 2 diuretic protocols. In chapter IV we address the overall important subject, and even more so in this andrological context, of the radioprotection related issues of a PET/CT with 18F-FDG. Finally, in chapter V we provide an overview of some of the issues still to be addressed and the future perspectives for this new direction in the field of nuclear medicine that we could name 'nuclear andrology'
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Pookhao, Naruekamol. "Statistical Methods for Functional Metagenomic Analysis Based on Next-Generation Sequencing Data." Diss., The University of Arizona, 2014. http://hdl.handle.net/10150/320986.
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Metagenomics is the study of a collective microbial genetic content recovered directly from natural (e.g., soil, ocean, and freshwater) or host-associated (e.g., human gut, skin, and oral) environmental communities that contain microorganisms, i.e., microbiomes. The rapid technological developments in next generation sequencing (NGS) technologies, enabling to sequence tens or hundreds of millions of short DNA fragments (or reads) in a single run, facilitates the studies of multiple microorganisms lived in environmental communities. Metagenomics, a relatively new but fast growing field, allows us to understand the diversity of microbes, their functions, cooperation, and evolution in a particular ecosystem. Also, it assists us to identify significantly different metabolic potentials in different environments. Particularly, metagenomic analysis on the basis of functional features (e.g., pathways, subsystems, functional roles) enables to contribute the genomic contents of microbes to human health and leads us to understand how the microbes affect human health by analyzing a metagenomic data corresponding to two or multiple populations with different clinical phenotypes (e.g., diseased and healthy, or different treatments). Currently, metagenomic analysis has substantial impact not only on genetic and environmental areas, but also on clinical applications. In our study, we focus on the development of computational and statistical methods for functional metagnomic analysis of sequencing data that is obtained from various environmental microbial samples/communities.
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Flöttmann, Max. "Functional analysis of High-Throughput data for dynamic modeling in eukaryotic systems." Doctoral thesis, Humboldt-Universität zu Berlin, Mathematisch-Naturwissenschaftliche Fakultät I, 2013. http://dx.doi.org/10.18452/16809.
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Das Verhalten Biologischer Systeme wird durch eine Vielzahl regulatorischer Prozesse beeinflusst, die sich auf verschiedenen Ebenen abspielen. Die Forschung an diesen Regulationen hat stark von den großen Mengen von Hochdurchsatzdaten profitiert, die in den letzten Jahren verfügbar wurden. Um diese Daten zu interpretieren und neue Erkenntnisse aus ihnen zu gewinnen, hat sich die mathematische Modellierung als hilfreich erwiesen. Allerdings müssen die Daten vor der Integration in Modelle aggregiert und analysiert werden. Wir präsentieren vier Studien auf unterschiedlichen zellulären Ebenen und in verschiedenen Organismen. Zusätzlich beschreiben wir zwei Computerprogramme die den Vergleich zwischen Modell und Experimentellen Daten erleichtern. Wir wenden diese Programme in zwei Studien über die MAP Kinase (MAP, engl. mitogen-acticated-protein) Signalwege in Saccharomyces cerevisiae an, um Modellalternativen zu generieren und unsere Vorstellung des Systems an Daten anzupassen. In den zwei verbleibenden Studien nutzen wir bioinformatische Methoden, um Hochdurchsatz-Zeitreihendaten von Protein und mRNA Expression zu analysieren. Um die Daten interpretieren zu können kombinieren wir sie mit Netzwerken und nutzen Annotationen um Module identifizieren, die ihre Expression im Lauf der Zeit ändern. Im Fall der humanen somatischen Zell Reprogrammierung führte diese Analyse zu einem probabilistischen Boolschen Modell des Systems, welches wir nutzen konnten um neue Hypothesen über seine Funktionsweise aufzustellen. Bei der Infektion von Säugerzellen (Canis familiaris) mit dem Influenza A Virus konnten wir neue Verbindungen zwischen dem Virus und seinem Wirt herausfinden und unsere Zeitreihendaten in bestehende Netzwerke einbinden. Zusammenfassend zeigen viele unserer Ergebnisse die Wichtigkeit von Datenintegration in mathematische Modelle, sowie den hohen Grad der Verschaltung zwischen verschiedenen Regulationssystemen.The behavior of all biological systems is governed by numerous regulatory mechanisms, acting on different levels of time and space. The study of these regulations has greatly benefited from the immense amount of data that has become available from high-throughput experiments in recent years. To interpret this mass of data and gain new knowledge about studied systems, mathematical modeling has proven to be an invaluable method. Nevertheless, before data can be integrated into a model it needs to be aggregated, analyzed, and the most important aspects need to be extracted. We present four Systems Biology studies on different cellular organizational levels and in different organisms. Additionally, we describe two software applications that enable easy comparison of data and model results. We use these in two of our studies on the mitogen-activated-protein (MAP) kinase signaling in Saccharomyces cerevisiae to generate model alternatives and adapt our representation of the system to biological data. In the two remaining studies we apply Bioinformatic methods to analyze two high-throughput time series on proteins and mRNA expression in mammalian cells. We combine the results with network data and use annotations to identify modules and pathways that change in expression over time to be able to interpret the datasets. In case of the human somatic cell reprogramming (SCR) system this analysis leads to the generation of a probabilistic Boolean model which we use to generate new hypotheses about the system. In the last system we examined, the infection of mammalian (Canis familiaris) cells by the influenza A virus, we find new interconnections between host and virus and are able to integrate our data with existing networks. In summary, many of our findings show the importance of data integration into mathematical models and the high degree of connectivity between different levels of regulation.
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Monnot, Cyril Gerard Valery. "Development of a data analysis platform for characterizing functional connectivity networks in rodents." Thesis, KTH, Skolan för teknik och hälsa (STH), 2013. http://urn.kb.se/resolve?urn=urn:nbn:se:kth:diva-124391.
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This document addresses the development and implementation of a routine for analyzing resting-state functional Magnetic Resonance Imaging (rs-fMRI) data in rodents. Even though resting-state connectivity is studied in humans already for several years with diverse applications in mental disorders or degenerative brain diseases, the interest for this modality is much more recent and less common in rodents. The goal of this project is to set an ensemble of tools in order to be able for the experimental MR team of KERIC to analyze rs-fMRI in rodents in a well defined and easy way. During this project several critical choices have been done, one of them is to use the Independent Component Analysis (ICA) in order to process the data rather than a seed-based approach. Also it was decided to use medetomidine as anesthesia rather than isoflurane for the experiments. The routine developed during this project was applied for a project studying the effects of running on an animal model of depression. The routine is composed of several steps, the preprocessing of the data mainly realized with SPM8, the processing using GIFT and the postprocessing which is some statistic tests on the results from GIFT in order to reveal differences between groups using the 2nd level analysis from SPM8 and the testing the correlations between components using the FNC toolbox.Detta dokument behandlar utvecklingen och implementeringen av en rutin för att analysera bilder från resting-state funktionell Magnetisk Resonenstomografi i gnagare. Även om resting-state connectivity studerats i människor i några år, med olika applikationer i psykiska störningar och neurodegenerativa sjukdomar, är intresset för detta område är betydligt nyare bland experimentell förskare som arbetar med gnagare. Målet av denna projekt är att inställa en procedur så att KERICs experimentell MR team kan lätt analysera resting-state funktionnell MRT data. Under denna projekt har olika viktiga val gjorts, en av dem är att använda Independent Component Analysis procedur för att analysera data framför en seed-baserad teknik. En andra var att använda för anestesi medetomidin och inte isofluran för experiment. Rutinen som var utvecklad under denna projekt blev användad på data från en projekt som studerar effekter av löpning på depression hos råttorna. Rutinen är delad i några delar, den första är att förbehandla data främst med SPM8, den andra är att använda GIFT för att behandla data och den sista är att testa statistiskt resultat från ICA med SPM8 och att testa korrelation mellan komponenter med FNC.
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Lu, Rong. "Statistical Methods for Functional Genomics Studies Using Observational Data." The Ohio State University, 2016. http://rave.ohiolink.edu/etdc/view?acc_num=osu1467830759.
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Schwartz, Yannick. "Large-scale functional MRI analysis to accumulate knowledge on brain functions." Thesis, Paris 11, 2015. http://www.theses.fr/2015PA112056/document.
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Comment peut-on accumuler de la connaissance sur les fonctions cérébrales ? Comment peut-on bénéficier d'années de recherche en IRM fonctionnelle (IRMf) pour analyser des processus cognitifs plus fins et construire un modèle exhaustif du cerveau ? Les chercheurs se basent habituellement sur des études individuelles pour identifier des régions cérébrales recrutées par les processus cognitifs. La comparaison avec l'historique du domaine se fait généralement manuellement pas le biais de la littérature, qui permet de définir des régions d'intérêt dans le cerveau. Les méta-analyses permettent de définir des méthodes plus formelles et automatisables pour analyser la littérature. Cette thèse examine trois manières d'accumuler et d'organiser les connaissances sur le fonctionnement du cerveau en utilisant des cartes d'activation cérébrales d'un grand nombre d'études. Premièrement, nous présentons une approche qui utilise conjointement deux expériences d'IRMf similaires pour mieux conditionner une analyse statistique. Nous montrons que cette méthode est une alternative intéressante par rapport aux analyses qui utilisent des régions d'intérêts, mais demande cependant un travail manuel dans la sélection des études qui l'empêche de monter à l'échelle. A cause de la difficulté à sélectionner automatiquement les études, notre deuxième contribution se focalise sur l'analyse d'une unique étude présentant un grand nombre de conditions expérimentales. Cette méthode estime des réseaux fonctionnels (ensemble de régions cérébrales) et les associe à des profils fonctionnels (ensemble pondéré de descripteurs cognitifs). Les limitations de cette approche viennent du fait que nous n'utilisons qu'une seule étude, et qu'elle se base sur un modèle non supervisé qui est par conséquent plus difficile à valider. Ce travail nous a cependant apporté la notion de labels cognitifs, qui est centrale pour notre dernière contribution. Cette dernière contribution présente une méthode qui a pour objectif d'apprendre des atlas fonctionnels en combinant plusieurs jeux de données. [Henson2006] montre qu'une inférence directe, c.a.d. la probabilité d'une activation étant donné un processus cognitif, n'est souvent pas suffisante pour conclure sur l'engagement de régions cérébrales pour le processus cognitif en question. Réciproquement, [Poldrack 2006] présente l'inférence inverse qui est la probabilité qu'un processus cognitif soit impliqué étant donné qu'une région cérébrale est activée, et décrit le risque de raisonnements fallacieux qui peuvent en découler. Pour éviter ces problèmes, il ne faut utiliser l'inférence inverse que dans un contexte où l'on suffisamment bien échantillonné l'espace cognitif pour pouvoir faire une inférence pertinente. Nous présentons une méthode qui utilise un « meta-design » pour décrire des tâches cognitives avec un vocabulaire commun, et qui combine les inférences directe et inverse pour mettre en évidence des réseaux fonctionnels qui sont cohérents à travers les études. Nous utilisons un modèle prédictif pour l'inférence inverse, et effectuons les prédictions sur de nouvelles études pour s'assurer que la méthode n'apprend pas certaines idiosyncrasies des données d'entrées. Cette dernière contribution nous a permis d'apprendre des réseaux fonctionnels, et de les associer avec des concepts cognitifs. Nous avons exploré différentes approches pour analyser conjointement des études d'IRMf. L'une des difficultés principales était de trouver un cadre commun qui permette d'analyser ensemble ces études malgré leur diversité. Ce cadre s'est instancié sous la forme d'un vocabulaire commun pour décrire les tâches d'IRMf. et a permis d'établir un modèle statistique du cerveau à grande échelle et d'accumuler des connaissances à travers des études d'IRM fonctionnelleHow can we accumulate knowledge on brain functions? How can we leverage years of research in functional MRI to analyse finer-grained psychological constructs, and build a comprehensive model of the brain? Researchers usually rely on single studies to delineate brain regions recruited by mental processes. They relate their findings to previous works in an informal way by defining regions of interest from the literature. Meta-analysis approaches provide a more principled way to build upon the literature. This thesis investigates three ways to assemble knowledge using activation maps from a large amount of studies. First, we present an approach that uses jointly two similar fMRI experiments, to better condition an analysis from a statistical standpoint. We show that it is a valuable data-driven alternative to traditional regions of interest analyses, but fails to provide a systematic way to relate studies, and thus does not permit to integrate knowledge on a large scale. Because of the difficulty to associate multiple studies, we resort to using a single dataset sampling a large number of stimuli for our second contribution. This method estimates functional networks associated with functional profiles, where the functional networks are interacting brain regions and the functional profiles are a weighted set of cognitive descriptors. This work successfully yields known brain networks and automatically associates meaningful descriptions. Its limitations lie in the unsupervised nature of this method, which is more difficult to validate, and the use of a single dataset. It however brings the notion of cognitive labels, which is central to our last contribution. Our last contribution presents a method that learns functional atlases by combining several datasets. [Henson 2006] shows that forward inference, i.e. the probability of an activation given a cognitive process, is often not sufficient to conclude on the engagement of brain regions for a cognitive process. Conversely, [Poldrack 2006] describes reverse inference as the probability of a cognitive process given an activation, but warns of a logical fallacy in concluding on such inference from evoked activity. Avoiding this issue requires to perform reverse inference with a large coverage of the cognitive space. We present a framework that uses a "meta-design" to describe many different tasks with a common vocabulary, and use forward and reverse inference in conjunction to outline functional networks that are consistently represented across the studies. We use a predictive model for reverse inference, and perform prediction on unseen studies to guarantee that we do not learn studies' idiosyncrasies. This final contribution permits to learn functional atlases, i.e. functional networks associated with a cognitive concept. We explored different possibilities to jointly analyse multiple fMRI experiments. We have found that one of the main challenges is to be able to relate the experiments with one another. As a solution, we propose a common vocabulary to describe the tasks. [Henson 2006] advocates the use of forward and reverse inference in conjunction to associate cognitive functions to brain regions, which is only possible in the context of a large scale analysis to overcome the limitations of reverse inference. This framing of the problem therefore makes it possible to establish a large statistical model of the brain, and accumulate knowledge across functional neuroimaging studies
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Leung, Tsui-shan, and 梁翠珊. "A functional analysis of GIS for slope management in Hong Kong." Thesis, The University of Hong Kong (Pokfulam, Hong Kong), 2000. http://hub.hku.hk/bib/B31223072.
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Wang, Chia-Wei, and 王嘉韋. "Functional Data of Discriminant Analysis." Thesis, 2007. http://ndltd.ncl.edu.tw/handle/62357397763760385791.
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碩士逢甲大學
統計與精算所
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Research this thesis is it is analysis function materials of attitude to come to analysis with discriminant analysis of multivariate analysis,the materials of the function type attitude are quite common in daily life, for example: Financial finance: Various kinds of that the company accumulates for a long time deal in data,Archaeology: Excavate by classification of fossil or bone,can by before appearance of bone excavating already describe materials classification of doing proper one, Medical science: Follow the trail of the patients physiological data for a long time,Others：The handwritten signature appraises the true and false、Sweep the data of taking aim in criminals shape of face、average materials of Temperature or rainfall moon which the regional weather collects station …etc.Can all be regarded as the function type materials, change specially, so as to get the effect of analysis. Foundation Ramsay and Silverman (2005,Ch8~11),use the multivariate analysis to functional data：Principal Components Analysis、Canonical Correlation Anaiysis、 Cluster Analysis、Discriminant Analysis. This research is to rely mainly on Discriminant Analysis.
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Backenroth, Daniel. "Methods in functional data analysis and functional genomics." Thesis, 2018. https://doi.org/10.7916/D81R82FM.
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This thesis has two overall themes, both of which involve the word functional, albeit in different contexts. The theme that motivates two of the chapters is the development of methods that enable a deeper understanding of the variability of functional data. The theme of the final chapter is the development of methods that enable a deeper understanding of the landscape of functionality across the human genome in different human tissues.
The first chapter of this thesis provides a framework for quantifying the variability of functional data and for analyzing the factors that affect this variability. We extend functional principal components analysis by modeling the variance of principal component scores. We pose a Bayesian model, which we estimate using variational Bayes methods. We illustrate our model with an application to a kinematic dataset of two-dimensional planar reaching motions by healthy subjects, showing the effect of learning on motion variability.
The second chapter of this thesis provides an alternative method for decomposing functional data that follows a Poisson distribution. Classical methods pose a latent Gaussian process that is then linked to the observed data via a logarithmic link function. We pose an alternative model that draws on ideas from non-negative matrix factorization, in which we constrain both scores and spline coefficient vectors for the functional prototypes to be non-negative. We impose smoothness on the functional prototypes. We estimate our model using the method of alternating minimization. We illustrate our model with an application to a dataset of accelerometer readings from elderly healthy Americans.
The third chapter of this thesis focuses on functional genomics, rather than functional data analysis. Here we pose a method for unsupervised clustering of functional genomics data. Our method is non-parametric, allowing for flexible modeling of the functional genomics data without binarization. We estimate our model using variational Bayes methods, and illustrate it by calculating genome-wide functional scores (based on a partition of our clusters into functional and non-functional clusters) for 127 different human tissues. We show that these genome-wide and tissue-specific functional scores provide state-of-the-art functional prediction.