Tesis sobre el tema "Hierarchical variables"
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Auyang, Arick Gin-Yu. "Robustness and hierarchical control of performance variables through coordination during human locomotion". Diss., Georgia Institute of Technology, 2010. http://hdl.handle.net/1853/42837.
Texto completoRIGGI, DANIELE. "Mixture factor model for hierarchical data structure and applications to the italian educational school system". Doctoral thesis, Università degli Studi di Milano-Bicocca, 2011. http://hdl.handle.net/10281/19465.
Texto completoChastaing, Gaëlle. "Indices de Sobol généralisés par variables dépendantes". Thesis, Grenoble, 2013. http://www.theses.fr/2013GRENM046.
Texto completoA mathematical model aims at characterizing a complex system or process that is too expensive to experiment. However, in this model, often strongly non linear, input parameters can be affected by a large uncertainty including errors of measurement of lack of information. Global sensitivity analysis is a stochastic approach whose objective is to identify and to rank the input variables that drive the uncertainty of the model output. Through this analysis, it is then possible to reduce the model dimension and the variation in the output of the model. To reach this objective, the Sobol indices are commonly used. Based on the functional ANOVA decomposition of the output, also called Hoeffding decomposition, they stand on the assumption that the incomes are independent. Our contribution is on the extension of Sobol indices for models with non independent inputs. In one hand, we propose a generalized functional decomposition, where its components is subject to specific orthogonal constraints. This decomposition leads to the definition of generalized sensitivity indices able to quantify the dependent inputs' contribution to the model variability. On the other hand, we propose two numerical methods to estimate these constructed indices. The first one is well-fitted to models with independent pairs of dependent input variables. The method is performed by solving linear system involving suitable projection operators. The second method can be applied to more general models. It relies on the recursive construction of functional systems satisfying the orthogonality properties of summands of the generalized decomposition. In parallel, we illustrate the two methods on numerical examples to test the efficiency of the techniques
Pfister, Mark. "Distribution of a Sum of Random Variables when the Sample Size is a Poisson Distribution". Digital Commons @ East Tennessee State University, 2018. https://dc.etsu.edu/etd/3459.
Texto completoHay, John Leslie. "Statistical modelling for non-Gaussian time series data with explanatory variables". Thesis, Queensland University of Technology, 1999.
Buscar texto completoGebremeskel, Haftu Gebrehiwot. "Implementing hierarchical bayesian model to fertility data: the case of Ethiopia". Doctoral thesis, Università degli studi di Padova, 2016. http://hdl.handle.net/11577/3424458.
Texto completoBackground: L’Etiopia è una nazione divisa in 9 regioni amministrative (definite su base etnica) e due città. Si tratta di una nazione citata spesso come esempio di alta fecondità e rapida crescita demografica. Nonostante gli sforzi del governo, fecondità e cresita della popolazione rimangono elevati, specialmente a livello regionale. Pertanto, lo studio della fecondità in Etiopia e nelle sue regioni – caraterizzate da un’alta variabilità – è di vitale importanza. Un modo semplice di rilevare le diverse caratteristiche della distribuzione della feconditàè quello di costruire in modello adatto, specificando diverse funzioni matematiche. In questo senso, vale la pena concentrarsi sui tassi specifici di fecondità, i quali mostrano una precisa forma comune a tutte le popolazioni. Tuttavia, molti paesi mostrano una “simmetrizzazione” che molti modelli non riescono a cogliere adeguatamente. Pertanto, per cogliere questa la forma dei tassi specifici, sono stati utilizzati alcuni modelli parametrici ma l’uso di tali modelliè ancora molto limitato in Africa ed in Etiopia in particolare. Obiettivo: In questo lavoro si utilizza un nuovo modello per modellare la fecondità in Etiopia con quattro obiettivi specifici: (1). esaminare la forma dei tassi specifici per età dell’Etiopia a livello nazionale e regionale; (2). proporre un modello che colga al meglio le varie forme dei tassi specifici sia a livello nazionale che regionale. La performance del modello proposto verrà confrontata con quella di altri modelli esistenti; (3). adattare la funzione di fecondità proposta attraverso un modello gerarchico Bayesiano e mostrare che tale modelloè sufficientemente flessibile per stimare la fecondità delle singole regioni – dove le stime possono essere imprecise a causa di una bassa numerosità campionaria; (4). confrontare le stime ottenute con quelle fornite da metodi non gerarchici (massima verosimiglianza o Bayesiana semplice) Metodologia: In questo studio, proponiamo un modello a 4 parametri, la Normale Asimmetrica, per modellare i tassi specifici di fecondità. Si mostra che questo modello è sufficientemente flessibile per cogliere adeguatamente le forme dei tassi specifici a livello sia nazionale che regionale. Per valutare la performance del modello, si è condotta un’analisi preliminare confrontandolo con altri dieci modelli parametrici e non parametrici usati nella letteratura demografica: la funzione splie quadratica, la Cubic-Spline, i modelli di Coale e Trussel, Beta, Gamma, Hadwiger, polinomiale, Gompertz, Peristera-Kostaki e l’Adjustment Error Model. I modelli sono stati stimati usando i minimi quadrati non lineari (nls) e il Criterio d’Informazione di Akaike viene usato per determinarne la performance. Tuttavia, la stima per le singole regioni pu‘o risultare difficile in situazioni dove abbiamo un’alta variabilità della numerosità campionaria. Si propone, quindi di usare procedure gerarchiche che permettono di ottenere stime più affidabili rispetto ai modelli non gerarchici (“pooling” completo o “unpooling”) per l’analisi a livello regionale. In questo studia si formula un modello Bayesiano gerarchico ottenendo la distribuzione a posteriori dei parametri per i tassi di fecnodità specifici a livello regionale e relativa stima dell’incertezza. Altri metodi non gerarchici (Bayesiano semplice e massima verosimiglianza) vengono anch’essi usati per confronto. Gli algoritmi Gibbs Sampling e Metropolis-Hastings vengono usati per campionare dalla distribuzione a posteriori di ogni parametro. Anche il metodo del “Data Augmentation” viene utilizzato per ottenere le stime. La robustezza dei risultati viene controllata attraverso un’analisi di sensibilità e l’opportuna diagnostica della convergenza degli algoritmi viene riportata nel testo. In tutti i casi, si sono usate distribuzioni a priori non-informative. Risultati: I risutlati ottenuti dall’analisi preliminare mostrano che il modello Skew Normal ha il pi`u basso AIC nelle regioni Addis Ababa, Dire Dawa, Harari, Affar, Gambela, Benshangul-Gumuz e anche per le stime nazionali. Nelle altre regioni (Tigray, Oromiya, Amhara, Somali e SNNP) il modello Skew Normal non risulta il milgiore, ma comunque mostra un buon adattamento ai dati. Dunque, il modello Skew Normal risulta il migliore in 6 regioni su 11 e sui tassi specifici di tutto il paese. Conclusioni: Dunque, il modello Skew Normal risulta globalmente il migliore. Da questo risultato iniziale, siè partiti per costruire i modelli Gerachico Bayesiano, Bayesiano semplice e di massima verosimiglianza. Il risultato del confronto tra questi tre approcci è che il modello gerarchico fornisce stime più preciso rispetto agli altri.
Gardiner, Robert B. "The relationship between teacher qualifications and chemistry achievement in the context of other student and teacher/school variables : application of hierarchical linear modelling /". Thesis, National Library of Canada = Bibliothèque nationale du Canada, 1998. http://www.collectionscanada.ca/obj/s4/f2/dsk1/tape11/PQDD_0003/MQ42384.pdf.
Texto completoHan, Gang. "Modeling the output from computer experiments having quantitative and qualitative input variables and its applications". Columbus, Ohio : Ohio State University, 2008. http://rave.ohiolink.edu/etdc/view?acc%5Fnum=osu1228326460.
Texto completoSaves, Paul. "High dimensional multidisciplinary design optimization for eco-design aircraft". Electronic Thesis or Diss., Toulouse, ISAE, 2024. http://www.theses.fr/2024ESAE0002.
Texto completoNowadays, there has been significant and growing interest in improving the efficiency of vehicle design processes through the development of tools and techniques in the field of multidisciplinary design optimization (MDO). In fact, when optimizing both the aerodynamics and structures, one needs to consider the effect of the aerodynamic shape variables and structural sizing variables on the weight which also affects the fuel consumption. MDO arises as a powerful tool that can perform this trade-off automatically. The objective of the Ph. D project is to propose an efficient approach for solving an aero-structural wing optimization process at the conceptual design level. The latter is formulated as a constrained optimization problem that involves a large number of design variables (typically 700 variables). The targeted optimization approach is based on a sequential enrichment (typically efficient global optimization (EGO)), using an adaptive surrogate model. Kriging surrogate models are one of the most widely used in engineering problems to substitute time-consuming high fidelity models. EGO is a heuristic method, designed for the solution of global optimization problems that has performed well in terms of quality of the solution computed. However, like any other method for global optimization, EGO suffers from the curse of dimensionality, meaning that its performance is satisfactory on lower dimensional problems, but deteriorates as the dimensionality of the optimization search space increases. For realistic aircraft wing design problems, the typical size of the design variables exceeds 700 and, thus, trying to solve directly the problems using EGO is ruled out. In practical test cases, high dimensional MDO problems may possess a lower intrinsic dimensionality, which can be exploited for optimization. In this context, a feature mapping can then be used to map the original high dimensional design variable onto a sufficiently small design space. Most of the existing approaches in the literature use random linear mapping to reduce the dimension, sometimes active learning is used to build this linear embedding. Generalizations to non-linear subspaces are also proposed using the so-called variational autoencoder. For instance, a composition of Gaussian processes (GP), referred as deep GP, can be very useful. In this PhD thesis, we will investigate efficient parameterization tools to significantly reduce the number of design variables by using active learning technics. An extension of the method could be also proposed to handle mixed continuous and categorical inputs using some previous works on low dimensional problems. Practical implementations within the OpenMDAO framework (an open source MDO framework developed by NASA) are expected
Guin, Ophélie. "Méthodes bayésiennes semi-paramétriques d'extraction et de sélection de variables dans le cadre de la dendroclimatologie". Phd thesis, Université Paris Sud - Paris XI, 2011. http://tel.archives-ouvertes.fr/tel-00636704.
Texto completoRockwood, Nicholas John. "Estimating Multilevel Structural Equation Models with Random Slopes for Latent Covariates". The Ohio State University, 2019. http://rave.ohiolink.edu/etdc/view?acc_num=osu1554478681581538.
Texto completoJulião, Heloise Pavanato. "Abundância e distribuiçãoda baleia jubarte (Megaptera novaeangliae) na costa do Brasil". reponame:Repositório Institucional da FURG, 2013. http://repositorio.furg.br/handle/1/4023.
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População é a unidade fundamental da conservação e sua forma mais simples de monitoramento envolve a amostragem temporal regular para a determinação do status populacional. Uma das populações de baleia jubarte do Hemisfério Sul utiliza a costa do Brasil entre maio e dezembro para se reprodução e criação dos filhotes. Esta população, denominada “estoque reprodutivo A” pela Comissão Internacional da Baleia, tem mostrado sinais de recuperação após um marcado declínio devido a caça e um longo período de moratória. Esta população se concentra principalmente no Banco dos Abrolhos (BA), onde águas calmas e quentes parecem constituir um hábitat ideal. Este estudo teve o objetivo de estimar o tamanho da população de jubartes para o ano de 2011, bem como predizer a distribuição de grupos na costa brasileira. O método de amostragem de distâncias foi implementado, e modelos hierárquicos Bayesianos foram propostos para estimar a abundância. Modelos auto-regressivos condicionais foram aplicados para predizer a densidade em células de 0.5° de latitude e longitude. O tamanho da população foi estimado em 10,160 baleias (Cr.I.95%=6,607-17,692). As maiores densidades foram encontradas entre o Banco dos Abrolhos e a Baía de Todos os Santos (BA). Os resultados sugerem que o aumento populacional acarreta a expansão da população para além do Banco dos Abrolhos.
Population is the fundamental unit of conservation and its simplest monitoring tool involves regular sampling over time for population assessing status. One of the Southern Hemisphere humpback whale populations winters at the Brazilian coast typically from May to December where breeding and calving occur. This population, labeled as “breeding stock A” by International Whaling Commission, has shown signs of recovery after the long period of whaling. The goal of this study was to estimate the population size of humpback whales up to 2011, and predict group distribution along the Brazilian coast. Distance sampling methods were implemented and hierarchical Bayesian models were proposed to estimate abundance. Conditional auto-regressive models were used to predict the density in a lattice of 0.5° of latitude and longitude. Population size was estimated at 10,160 whales (Cr.I.95%=6,607-17,692). Highest densities were predicted to occur between Abrolhos Bank and Todos os Santos Bay (BA). The results suggest that the population increase leads to a population expansion beyond Abrolhos Bank.
Frühwirth-Schnatter, Sylvia y Regina Tüchler. "Bayesian parsimonious covariance estimation for hierarchical linear mixed models". Institut für Statistik und Mathematik, WU Vienna University of Economics and Business, 2004. http://epub.wu.ac.at/774/1/document.pdf.
Texto completoSeries: Research Report Series / Department of Statistics and Mathematics
Chao, Yi. "Bayesian Hierarchical Latent Model for Gene Set Analysis". Thesis, Virginia Tech, 2009. http://hdl.handle.net/10919/32060.
Texto completoMaster of Science
Robbins, Donald H. "Hierarchical modeling of laminated composite plates using variable kinematic finite elements and mesh superposition". Diss., Virginia Tech, 1993. http://hdl.handle.net/10919/40117.
Texto completoStone, Elizabeth Anne. "Multilevel Model Selection: A Regularization Approach Incorporating Heredity Constraints". Diss., Temple University Libraries, 2013. http://cdm16002.contentdm.oclc.org/cdm/ref/collection/p245801coll10/id/234414.
Texto completoPh.D.
This dissertation focuses on estimation and selection methods for a simple linear model with two levels of variation. This model provides a foundation for extensions to more levels. We propose new regularization criteria for model selection, subset selection, and variable selection in this context. Regularization is a penalized-estimation approach that shrinks the estimate and selects variables for structured data. This dissertation introduces a procedure (HM-ALASSO) that extends regularized multilevel-model estimation and selection to enforce principles of fixed heredity (e.g., including main effects when their interactions are included) and random heredity (e.g., including fixed effects when their random terms are included). The goals in developing this method were to create a procedure that provided reasonable estimates of all parameters, adhered to fixed and random heredity principles, resulted in a parsimonious model, was theoretically justifiable, and was able to be implemented and used in available software. The HM-ALASSO incorporates heredity-constrained selection directly into the estimation process. HM-ALASSO is shown to enjoy the properties of consistency, sparsity, and asymptotic normality. The ability of HM-ALASSO to produce quality estimates of the underlying parameters while adhering to heredity principles is demonstrated using simulated data. The performance of HM-ALASSO is illustrated using a subset of the High School and Beyond (HS&B) data set that includes math-achievement outcomes modeled via student- and school-level predictors. The HM-ALASSO framework is flexible enough that it can be adapted for various rule sets and parameterizations.
Temple University--Theses
Jiang, Bo. "Partition Models for Variable Selection and Interaction Detection". Thesis, Harvard University, 2013. http://dissertations.umi.com/gsas.harvard:10911.
Texto completoStatistics
Šulc, Zdeněk. "Similarity Measures for Nominal Data in Hierarchical Clustering". Doctoral thesis, Vysoká škola ekonomická v Praze, 2013. http://www.nusl.cz/ntk/nusl-261939.
Texto completoPirathiban, Ramethaa. "Improving species distribution modelling: Selecting absences and eliciting variable usefulness for input into standard algorithms or a Bayesian hierarchical meta-factor model". Thesis, Queensland University of Technology, 2019. https://eprints.qut.edu.au/134401/1/Ramethaa_Pirathiban_Thesis.pdf.
Texto completoCharalambous, Christiana. "Variable selection in joint modelling of mean and variance for multilevel data". Thesis, University of Manchester, 2011. https://www.research.manchester.ac.uk/portal/en/theses/variable-selection-in-joint-modelling-of-mean-and-variance-for-multilevel-data(cbe5eb08-1e77-4b44-b7df-17bd4bf4937f).html.
Texto completoRaeli, Alice. "Solution of the variable coefficients Poisson equation on Cartesian hierarchical meshes in parallel : applications to phase changing materials". Thesis, Bordeaux, 2017. http://www.theses.fr/2017BORD0669/document.
Texto completoWe consider problems governed by a linear elliptic equation with varying coéficients across internal interfaces. The solution and its normal derivative can undergo significant variations through these internal boundaries. We present a compact finite-difference scheme on a tree-based adaptive grid that can be efficiently solved using a natively parallel data structure. The main idea is to optimize the truncation error of the discretization scheme as a function of the local grid configuration to achieve second order accuracy. Numerical illustrations relevant for actual applications are presented in two and three-dimensional configurations
Kwon, Hyukje. "A Monte Carlo Study of Missing Data Treatments for an Incomplete Level-2 Variable in Hierarchical Linear Models". The Ohio State University, 2011. http://rave.ohiolink.edu/etdc/view?acc_num=osu1303846627.
Texto completoHuo, Shuning. "Bayesian Modeling of Complex High-Dimensional Data". Diss., Virginia Tech, 2020. http://hdl.handle.net/10919/101037.
Texto completoDoctor of Philosophy
With the rapid development of modern high-throughput technologies, scientists can now collect high-dimensional data in different forms, such as engineering signals, medical images, and genomics measurements. However, acquisition of such data does not automatically lead to efficient knowledge discovery. The main objective of this dissertation is to develop novel Bayesian methods to extract useful knowledge from complex high-dimensional data. It has two parts—the development of an ultra-fast functional mixed model and the modeling of data heterogeneity via Dirichlet Diffusion Trees. The first part focuses on developing approximate Bayesian methods in functional mixed models to estimate parameters and detect significant regions. Two datasets demonstrate the effectiveness of proposed method—a mass spectrometry dataset in a cancer study and a neuroimaging dataset in an Alzheimer's disease study. The second part focuses on modeling data heterogeneity via Dirichlet Diffusion Trees. The method helps uncover the underlying hierarchical tree structures and estimate systematic differences between the group of samples. We demonstrate the effectiveness of the method through the brain tumor imaging data.
Trahan, Patrick. "Classification of Carpiodes Using Fourier Descriptors: A Content Based Image Retrieval Approach". ScholarWorks@UNO, 2009. http://scholarworks.uno.edu/td/1085.
Texto completoHuang, Huei-Ching y 黃慧青. "Latent Class Model with Two Hierarchical Latent Variables". Thesis, 2005. http://ndltd.ncl.edu.tw/handle/12163370355322189586.
Texto completo"Bayesian analysis of generalized latent variable models with hierarchical data". Thesis, 2009. http://library.cuhk.edu.hk/record=b6075429.
Texto completoThesis (Ph.D.)--Chinese University of Hong Kong, 2009.
Includes bibliographical references (leaves 121-135).
Electronic reproduction. Hong Kong : Chinese University of Hong Kong, [2012] System requirements: Adobe Acrobat Reader. Available via World Wide Web.
Abstract also in Chinese.
BIONDI, LUIGI. "Identifiability of Discrete Hierarchical Models with One Latent Variable". Doctoral thesis, 2016. http://hdl.handle.net/2158/1028810.
Texto completo"Multiple Imputation for Two-Level Hierarchical Models with Categorical Variables and Missing at Random Data". Doctoral diss., 2016. http://hdl.handle.net/2286/R.I.40705.
Texto completoDissertation/Thesis
Doctoral Dissertation Educational Psychology 2016
"Type I and type II error in hierarchical analysis of variance using logistic regression for dichotomous dependent variables". Tulane University, 1992.
Buscar texto completoacase@tulane.edu
Yurecko, Michele. "Investigating the relationship between reading achievement, and state-level ecological variables and educational reform a hierarchical analysis of item difficulty variation /". 2009. http://hdl.rutgers.edu/1782.2/rucore10001600001.ETD.000051083.
Texto completoLemyre, Gabriel. "Modèles de Markov à variables latentes : matrice de transition non-homogène et reformulation hiérarchique". Thesis, 2021. http://hdl.handle.net/1866/25476.
Texto completoThis master’s thesis is centered on the Hidden Markov Models, a family of models in which an unobserved Markov chain dictactes the behaviour of an observable stochastic process through which a noisy version of the latent chain is observed. These bivariate stochastic processes that can be seen as a natural generalization of mixture models have shown their ability to capture the varying dynamics of many time series and, more specifically in finance, to reproduce the stylized facts of financial returns. In particular, we are interested in discrete-time Markov chains with finite state spaces, with the objective of studying the contribution of their hierarchical formulations and the relaxation of the homogeneity hypothesis for the transition matrix to the quality of the fit and predictions, as well as the capacity to reproduce the stylized facts. We therefore present two hierarchical structures, the first allowing for new interpretations of the relationships between states of the chain, and the second allowing for a more parsimonious parameterization of the transition matrix. We also present three non-homogeneous models, two of which have transition probabilities dependent on observed explanatory variables, and the third in which the probabilities depend on another latent variable. We first analyze the goodness of fit and the predictive power of our models on the series of log returns of the S&P 500 and the exchange rate between canadian and american currencies (CADUSD). We also illustrate their capacity to reproduce the stylized facts, and present interpretations of the estimated parameters for the hierarchical and non-homogeneous models. In general, our results seem to confirm the contribution of hierarchical and non-homogeneous models to these measures of performance. In particular, these results seem to suggest that the incorporation of non-homogeneous dynamics to a hierarchical structure may allow for a more faithful reproduction of the stylized facts—even the slow decay of the autocorrelation functions of squared and absolute returns—and better predictive power, while still allowing for the interpretation of the estimated parameters.
CASSESE, ALBERTO. "A Hierarchical Bayesian Modeling Approach To Genetical Genomics". Doctoral thesis, 2013. http://hdl.handle.net/2158/794601.
Texto completoLin, Lin. "Bayesian Variable Selection in Clustering and Hierarchical Mixture Modeling". Diss., 2012. http://hdl.handle.net/10161/5846.
Texto completoClustering methods are designed to separate heterogeneous data into groups of similar objects such that objects within a group are similar, and objects in different groups are dissimilar. From the machine learning perspective, clustering can also be viewed as one of the most important topics within the unsupervised learning problem, which involves finding structures in a collection of unlabeled data. Various clustering methods have been developed under different problem contexts. Specifically, high dimensional data has stimulated a high level of interest in combining clustering algorithms and variable selection procedures; large data sets with expanding dimension have provoked an increasing need for relevant, customized clustering algorithms that offer the ability to detect low probability clusters.
This dissertation focuses on the model-based Bayesian approach to clustering. I first develop a new Bayesian Expectation-Maximization algorithm in fitting Dirichlet process mixture models and an algorithm to identify clusters under mixture models by aggregating mixture components. These two algorithms are used extensively throughout the dissertation. I then develop the concept and theory of a new variable selection method that is based on an evaluation of subsets of variables for the discriminatory evidence they provide in multivariate mixture modeling. This new approach to discriminative information analysis uses a natural measure of concordance between mixture component densities. The approach is both effective and computationally attractive for routine use in assessing and prioritizing subsets of variables according to their roles in the discrimination of one or more clusters. I demonstrate that the approach is useful for providing an objective basis for including or excluding specific variables in flow cytometry data analysis. These studies demonstrate how ranked sets of such variables can be used to optimize clustering strategies and selectively visualize identified clusters of the data of interest.
Next, I create a new approach to Bayesian mixture modeling with large data sets for a specific, important class of problems in biological subtype identification. The context, that of combinatorial encoding in flow cytometry, naturally introduces the hierarchical structure that these new models are designed to incorporate. I describe these novel classes of Bayesian mixture models with hierarchical structures that reflect the underlying problem context. The Bayesian analysis involves structured priors and computations using customized Markov chain Monte Carlo methods for model fitting that exploit a distributed GPU (graphics processing unit) implementation. The hierarchical mixture model is applied in the novel use of automated flow cytometry technology to measure levels of protein markers on thousands to millions of cells.
Finally, I develop a new approach to cluster high dimensional data based on Kingman's coalescent tree modeling ideas. Under traditional clustering models, the number of parameters required to construct the model increases exponentially with the number of dimensions. This phenomenon can lead to model overfitting and an enormous computational search challenge. The approach addresses these issues by proposing to learn the data structure in each individual dimension and combining these dimensions in a flexible tree-based model class. The new tree-based mixture model is studied extensively under various simulation studies, under which the model's superiority is reflected compared with traditional mixture models.
Dissertation
Li, Yingbo. "Bayesian Hierarchical Models for Model Choice". Diss., 2013. http://hdl.handle.net/10161/8063.
Texto completoWith the development of modern data collection approaches, researchers may collect hundreds to millions of variables, yet may not need to utilize all explanatory variables available in predictive models. Hence, choosing models that consist of a subset of variables often becomes a crucial step. In linear regression, variable selection not only reduces model complexity, but also prevents over-fitting. From a Bayesian perspective, prior specification of model parameters plays an important role in model selection as well as parameter estimation, and often prevents over-fitting through shrinkage and model averaging.
We develop two novel hierarchical priors for selection and model averaging, for Generalized Linear Models (GLMs) and normal linear regression, respectively. They can be considered as "spike-and-slab" prior distributions or more appropriately "spike- and-bell" distributions. Under these priors we achieve dimension reduction, since their point masses at zero allow predictors to be excluded with positive posterior probability. In addition, these hierarchical priors have heavy tails to provide robust- ness when MLE's are far from zero.
Zellner's g-prior is widely used in linear models. It preserves correlation structure among predictors in its prior covariance, and yields closed-form marginal likelihoods which leads to huge computational savings by avoiding sampling in the parameter space. Mixtures of g-priors avoid fixing g in advance, and can resolve consistency problems that arise with fixed g. For GLMs, we show that the mixture of g-priors using a Compound Confluent Hypergeometric distribution unifies existing choices in the literature and maintains their good properties such as tractable (approximate) marginal likelihoods and asymptotic consistency for model selection and parameter estimation under specific values of the hyper parameters.
While the g-prior is invariant under rotation within a model, a potential problem with the g-prior is that it inherits the instability of ordinary least squares (OLS) estimates when predictors are highly correlated. We build a hierarchical prior based on scale mixtures of independent normals, which incorporates invariance under rotations within models like ridge regression and the g-prior, but has heavy tails like the Zeller-Siow Cauchy prior. We find this method out-performs the gold standard mixture of g-priors and other methods in the case of highly correlated predictors in Gaussian linear models. We incorporate a non-parametric structure, the Dirichlet Process (DP) as a hyper prior, to allow more flexibility and adaptivity to the data.
Dissertation
Xin-HanHuang y 黃信翰. "Application of Spatial Bayesian Hierarchical Model with Variable Selection to fMRI data". Thesis, 2015. http://ndltd.ncl.edu.tw/handle/18746413115126691555.
Texto completo國立成功大學
統計學系
103
We propose a spatial Bayesian hierarchical model to analyze functional magnetic resonance imaging data with complex spatial and temporal structures. Several studies have found that the spatial dependence not only appear in signal changes but also in temporal correlations among voxels. However, currently existing statistical approaches ignore the spatial dependence of temporal correlations for the computational efficiency. We consider the spatial random effect models to simultaneously model spatial dependences in both signal changes and temporal correlations, but keep computationally feasible. Through simulation, the proposed approach improves the accuracy of identifying the activations. We study the properties of the model through its performance on simulations and a real event-related fMRI data set.
CAVICCHIA, CARLO. "Hierarchical latent variable models for dimensionality reduction: an application on composite indicators". Doctoral thesis, 2020. http://hdl.handle.net/11573/1363237.
Texto completoMinto, Cóilín. "Ecological Inference from Variable Recruitment Data". 2011. http://hdl.handle.net/10222/13881.
Texto completoChen, Ting-Shiang y 陳庭祥. "Target Human Following Using Neural-Network-Based RFID Localization System with Hierarchical Variable Structure Control". Thesis, 2016. http://ndltd.ncl.edu.tw/handle/azy8r5.
Texto completo國立臺灣科技大學
電機工程系
104
At the beginning, the received signal strength indicators (RSSIs) of the three tags on a triangular pattern are read by two perpendicular antennas. These 6 RSSIs and their corresponding pose and the azimuth angle of target human (TH) with respect to automatic guided vehicle (AGV) are obtained. Since the relations of these pairs of input and output are nonlinear, coupled, and stochastic, it is difficult to obtain an effective model. A 1st-order low-pass filter with unit dc gain is first employed to remove the unnecessary high frequencies of RSSIs. Due to the advantageous features of neural network modeling, e.g., stochastic approximation, insensitive to noise, different numbers of input and output, the multilayer neural network (MLNN) with Levenberg-Marquard Back-Propagation (LMBP) learning law is employed to achieve the model between six filtered RSSIs and three outputs (i.e., the pose and the azimuth angle of TH). Then the trajectory to track the TH is on-line planned and predicted from the output of Multilayer Perceptron Network (MLPN). The hierarchical variable structure control (HVSC) is employed to on-line track the planning trajectory such that the TH following is achieved. For an effective implementation, a software/hardware based platform is employed to develop the software for the MLPN modeling, the trajectory planning algorithm and the HVSC algorithm, and the hardware for the control signal (e.g., the PWM for driving the motor) and for the sensor inputs (e.g., the decoder for obtaining the position or velocity of motor, the USB interface for receiving RFID signal). Finally, the experiments for the TH following by the proposed NN-based RFID localization system and HVSC algorithm confirm the effectiveness, efficiency, and robustness of the proposed method.
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Kaplan, Andrea Jean. "An overview of multilevel regression". Thesis, 2010. http://hdl.handle.net/2152/ETD-UT-2010-12-2462.
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Xu, Lizhen. "Bayesian Methods for Genetic Association Studies". Thesis, 2012. http://hdl.handle.net/1807/34972.
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