Dissertations / Theses on the topic 'Temporal Point Processes (TPPs)'

Dans le domaine de l'imagerie cérébrale non invasive, la magnéto- et l'électroencéphalographie (M/EEG) offrent un précieux aperçu des activités neuronales. Les données enregistrées consistent en des séries temporelles multivariées qui fournissent des informations sur les processus cognitifs et sont souvent complétées par des détails auxiliaires liés au paradigme expérimental, tels que l'horodatage des stimuli externes ou des actions entreprises par les sujets. En outre, l'ensemble des données peut inclure des enregistrements de plusieurs sujets, ce qui facilite les analyses en population.Cette thèse de doctorat présente un nouveau cadre pour l'analyse des signaux M/EEG qui synergise l'Apprentissage Convolutif de Dictionnaire (CDL) et les Processus Ponctuels Temporels (TPP). Ce travail est divisé en deux composantes principales : les avancées en modélisation temporelle et le passage à l'échelle computationnelle. En matière de modélisation temporelle, deux nouveaux modèles de processus ponctuels sont introduits, accompagnés de méthodes d'inférence efficaces pour capturer les activités neuronales liées aux tâches. La méthode proposée d'Inférence Discrétisée Rapide pour les Processus de Hawkes (FaDIn) a également des implications pour des applications plus larges. De plus, ce travail aborde les défis computationnels de l'analyse des données M/EEG à grande échelle basée sur le CDL, en introduisant un nouvel algorithme robuste de CDL avec fenêtrage stochastique. Cet algorithme permet de traiter efficacement les signaux entachés d'artefacts ainsi que les études de population à grande échelle. Le CDL populationnelle a ensuite été utilisée sur le grand ensemble de données en libre accès Cam-CAN, révélant des aspects de l'activité neuronale liée à l'âge
In the field of non-invasive brain imaging, Magnetoencephalography and Electroencephalography (M/EEG) offer invaluable insights into neural activities. The recorded data consist of multivariate time series that provide information about cognitive processes and are often complemented by auxiliary details related to the experimental paradigm, such as timestamps of external stimuli or actions undertaken by the subjects. Additionally, the dataset may include recordings from multiple subjects, facilitating population- level analyses.This doctoral research presents a novel framework for M/EEG signal analysis that synergizes Convolutional Dictionary Learning (CDL) and Temporal Point Processes (TPPs). The work is segmented into two primary components: temporal modeling advancements and computational scalability. For temporal modeling, two novel point process models are introduced with efficient inference methods to capture task-specific neural activities. The proposed Fast Discretized Inference for Hawkes Processes (FaDIn) method also has implications for broader applications. Additionally, this work addresses the computational challenges of large-scale M/EEG data CDL-based analysis, by introducing a novel Stochastic Robust Windowing CDL algorithm. This algorithm allows to process efficiently artifact-ridden signals as well as large population studies. Population CDL was then used on the large open-access dataset Cam-CAN, shedding light on age-related neural activity

Changepoint analysis is a well established area of statistical research, but in the context of spatio-temporal point processes it is as yet relatively unexplored. Some substantial differences with regard to standard changepoint analysis have to be taken into account: firstly, at every time point the datum is an irregular pattern of points; secondly, in real situations issues of spatial dependence between points and temporal dependence within time segments raise. Our motivating example consists of data concerning the monitoring and recovery of radioactive particles from Sandside beach, North of Scotland; there have been two major changes in the equipment used to detect the particles, representing known potential changepoints in the number of retrieved particles. In addition, offshore particle retrieval campaigns are believed may reduce the particle intensity onshore with an unknown temporal lag; in this latter case, the problem concerns multiple unknown changepoints. We therefore propose a Bayesian approach for detecting multiple changepoints in the intensity function of a spatio-temporal point process, allowing for spatial and temporal dependence within segments. We use Log-Gaussian Cox Processes, a very flexible class of models suitable for environmental applications that can be implemented using integrated nested Laplace approximation (INLA), a computationally efficient alternative to Monte Carlo Markov Chain methods for approximating the posterior distribution of the parameters. Once the posterior curve is obtained, we propose a few methods for detecting significant change points. We present a simulation study, which consists in generating spatio-temporal point pattern series under several scenarios; the performance of the methods is assessed in terms of type I and II errors, detected changepoint locations and accuracy of the segment intensity estimates. We finally apply the above methods to the motivating dataset and find good and sensible results about the presence and quality of changes in the process.

Changepoint analysis is a well established area of statistical research, but in the context of spatio-temporal point processes it is as yet relatively unexplored. Some substantial differences with regard to standard changepoint analysis have to be taken into account: firstly, at every time point the datum is an irregular pattern of points; secondly, in real situations issues of spatial dependence between points and temporal dependence within time segments raise. Our motivating example consists of data concerning the monitoring and recovery of radioactive particles from Sandside beach, North of Scotland; there have been two major changes in the equipment used to detect the particles, representing known potential changepoints in the number of retrieved particles. In addition, offshore particle retrieval campaigns are believed may reduce the particle intensity onshore with an unknown temporal lag; in this latter case, the problem concerns multiple unknown changepoints. We therefore propose a Bayesian approach for detecting multiple changepoints in the intensity function of a spatio-temporal point process, allowing for spatial and temporal dependence within segments. We use Log-Gaussian Cox Processes, a very flexible class of models suitable for environmental applications that can be implemented using integrated nested Laplace approximation (INLA), a computationally efficient alternative to Monte Carlo Markov Chain methods for approximating the posterior distribution of the parameters. Once the posterior curve is obtained, we propose a few methods for detecting significant change points. We present a simulation study, which consists in generating spatio-temporal point pattern series under several scenarios; the performance of the methods is assessed in terms of type I and II errors, detected changepoint locations and accuracy of the segment intensity estimates. We finally apply the above methods to the motivating dataset and find good and sensible results about the presence and quality of changes in the process.

Point processes are mechanisms that beget point patterns. Realisations of point processes are observed in many contexts, for example, locations of stars in the sky, or locations of trees in a forest. Inferring the mechanisms that drive point processes relies on the development of models that appropriately account for the dependencies inherent in the data. Fitting models that adequately capture the complex dependency structures in either space, time, or both is often problematic. This is commonly due to—but not restricted to—the intractability of the likelihood function, or computational burden of the required numerical operations. This thesis primarily focuses on developing point process models with some hierarchical structure, and specifically where this is a latent structure that may be considered as one of the following: (i) some unobserved construct assumed to be generating the observed structure, or (ii) some stochastic process describing the structure of the point pattern. Model fitting procedures utilised in this thesis include either (i) approximate-likelihood techniques to circumvent intractable likelihoods, (ii) stochastic partial differential equations to model continuous spatial latent structures, or (iii) improving computational speed in numerical approximations by exploiting automatic differentiation. Moreover, this thesis extends classic point process models by considering multivariate dependencies. This is achieved through considering a general class of joint point process model, which utilise shared stochastic structures. These structures account for the dependencies inherent in multivariate point process data. These models are applied to data originating from various scientific fields; in particular, applications are considered in ecology, medicine, and geology. In addition, point process models that account for the second order behaviour of these assumed stochastic structures are also considered.

Esta tesis se centra principalmente en el desarrollo de propiedades y características de los estimadores de segundo orden de procesos puntuales y espacio-temporales. En primer lugar, se presenta un marco teórico acerca de procesos puntuales espaciales y espacio-temporales. El resto de la tesis se organiza como sigue. En el capítulo 2, se presenta una nueva familia de kernel positivos y óptimos, además se propone un estimador insensgado alternativo para la función de la densidad del producto. Su rendimiento se compara para varios kernel mediante MISE. En el capítulo 3, se dada un nuevo estimador kernel de la función de la densidad producto espacio-temporal y también se desarrollan expresiones cerradas para la varianza en el caso de Poisson. En el Capítulo 4, nos centramos en los métodos de orientación de segundo orden los cuales proporcionan una herramienta para el análisis natural para los datos espaciales anisótropicos. Finalmente, se proporciona una descripción general de los proyectos de investigación actualmente en curso que han surgido motivadas por la estrecha relación con las propiedades de segundo orden de los procesos puntuales espaciales y espacio-temporales.
This thesis is mainly focused on developing properties and estimators for second-order characteristics of spatio-temporal point processes. First, we present a theoretical framework of spatial and spatio-temporal point processes. The rest of the thesis is organized as follows. In Chapter 2 we present a new family of optimal and positive kernels an alternative unbiased estimator for the product density function. Its performance is compare under several kernel through MISE. In Chapter 3 a new kernel estimator of spatio-temporal product density function are given and also are developed close expressions for the variance under the Poisson case. En el capítulo 4 nos centramos en los métodos de orientación de segundo orden que proporcionan una herramienta natural para el análisis de los datos de proceso Punto espaciales anisótropas. Finally, we provide a general description of the currently ongoing research projects which have emerged motivated by the close relationship with the second-order properties.

This thesis represents the ontological model for the Time Aspects for a Healthcare Organization. It provides information about activities which take place at different interval of time at Ryhov Hospital. These activities are series of actions which may be happen in predefined sequence and at predefined times or may be happen at any time in a General ward or in Emergency ward of a Ryhov Hospital.

For achieving above mentioned objective, our supervisor conducts a workshop at the start of thesis. In this workshop, the domain experts explain the main idea of ward activities. From this workshop; the author got a lot of knowledge about activities and time aspects. After this, the author start literature review for achieving valuable knowledge about ward activities, time aspects and also methodology steps which are essentials for ontological model. After developing ontological model for Time Aspects, our supervisor also conducts a second workshop. In this workshop, the author presents the model for evaluation purpose.

In this thesis, new models and methodologies are introduced for the analysis of dynamic processes characterized by image sequences with spatial temporal overlapping. The spatial temporal overlapping exists in many natural phenomena and should be addressed properly in several Science disciplines such as Microscopy, Material Sciences, Biology, Geostatistics or Communication Networks. This work is related to the Point Process and Random Closed Set theories, within Stochastic Geometry. The proposed models are an extension of Boolean Models in R2 by adding a temporal dimension. The study has been motivated for its application in a multidisciplinary project that combined Statistics, Computer Sciences, Biology and Microscopy, with the aim of analysing the cell exocytosis and endocytosis. Exocytosis is the process by which cells secrete vesicles outside the plasma membrane and endocytosis is the opposite mechanism. Our data were image sequences obtained by Electron Microscopy and Total Internal Reflection Fluorescence Microscopy. Fluorescent tagged-proteins are observed as overlapped clusters with random shape, area and duration. They can be modelled as realizations of a stationary and isotropic stochastic process. The methodology herein proposed could be used to analyze similar phenomena in other Fields of Science. First, the temporal Boolean model is introduced and some estimation methods for the parameters of the model are presented. Second, we proposed a method for the estimation of the event duration distribution function of a univariate temporal Boolean model based on spatial temporal covariance. A simulation study is performed with several duration probability density functions, and an application to the cell endocytosis is realized. Third, we introduce the bivariate temporal Boolean model to study interactions between two overlapped spatial temporal processes and to quantify their overlapping and dependencies. We propose a non-parametric approach based on a generalization of the Ripley K-function, the spatial-temporal covariance and the pair correlation functions for a bivariate temporal random closed set. A Monte Carlo test was performed to test the independence hypothesis. This methodology is not only a test procedure but also allows us to quantify the degree and spatial temporal interval of the interaction. No parametric assumption is needed. A simulation study has been conducted and an application to the study of proteins that mediate in cell endocytosis has been performed. Fourth, from high spatial resolution EM images, we model the distribution of exocytic vesicles (granules) within the cell cytoplasm as a realization of a finite point process (a point pattern), and the point patterns of several cell groups are considered replicates of different point processes. Our aim was to study differences between two treatment groups in terms of granule location. We characterize the spatial distribution of granules with respect to the plasma membrane by means of several functional descriptors, that allowed us to detect significant differences between the two cell groups that would not be observed by a classical approach. To perform image segmentation, we developed an automatic granule detection tool with similar performance to that of the manual one-by-one marking. Finally, we have implemented a software toolbox for the simulation and analysis of temporal Boolean models (available at http : ==www:uv:es=tracs=), so scientists and technicians of any discipline can apply the proposed methods. In summary, the spatial temporal stochastic models proposed allow modelling of dynamic processes from image sequences where several forms of random shape, size and duration overlap. It is the first time these tools are applied to the study of cell exo and endocytosis, and they would contribute to improve their understanding. Our methodologies will help future research in Cell Biology, e.g. in the study of diseases related to secretion dysfunctions, such as diabetes.
En esta tesis presentamos nuevos modelos y metodolog as para el an alisis de pro- cesos din amicos a partir de secuencias de im agenes, con solapamiento espacial y tem- poral de los objetos de an alisis, un fen omeno habitual en la naturaleza. El trabajo realizado se enmarca en la teor a de Procesos Puntuales y Conjuntos Aleatorios Ce- rrados (RACS), dentro de la Geometr a Estoc astica. Los modelos propuestos son una extensi on de la teor a de modelos booleanos en R2 incorporando una componente temporal. La motivaci on del trabajo fue su aplicaci on a un proyecto multidisciplinar donde analizamos la exocitosis y la endocitosis celular, procesos en que la c elula segrega o absorbe sustancias a trav es de la membrana citoplasm atica, respectivamente. El es- tudio se realiz o utilizando secuencias de im agenes obtenidas con microscop a TIRFM, donde se observan las prote nas como agrupaciones uorescentes superpuestas. Mo- delizamos las im agenes como realizaciones de un proceso estoc astico estacionario e isotr opico. Esta metodolog a permite analizar fen omenos reales en otros campos de la Ciencia con superposici on espacio-temporal de objetos con formas y duraciones aleatorias, como Geolog a, Qu mica, Comunicaciones, etc. Primero, introducimos el modelo booleano temporal. Presentamos un m etodo de estimaci on de la funci on de distribuci on de la duraci on basado en la covarianza espacio-temporal, y el estudio de simulaci on realizado. Segundo, estudiamos la in- terrelaci on entre dos procesos espacio-temporales mediante la K-funci on de Ripley, la covarianza espacio-temporal y la funci on de correlaci on para conjuntos aleatorios bivariados. Realizamos un estudio de simulaci on y una aplicaci on a la endocitosis celular. Tercero, modelizamos la distribuci on de ves culas exoc ticas (gr anulos) en el cito- plasma celular como un proceso puntual nito. Caracterizamos su distribuci on espa- cial respecto a la membrana mediante varios descriptores funcionales. Para segmentar las im agenes, desarrollamos una herramienta autom atica de detecci on de gr anulos. Hemos desarrollado una herramienta de software completa para la simulaci on y es- timaci on de modelos booleanos temporales (disponible en http : ==www:uv:es=tracs=).

Consideramos uma base de dados hospitalares constituída por informações sobre vítimas de causas externas atendidas no Pronto Socorro do Hospital Municipal Dr. Arthur Ribeiro de Saboya, no período de 01/01/02 a 11/01/03, e registradas pelo Núcleo de Atenção à Vítima de Violência deste hospital. O conjunto de dados foi avaliado sob duas abordagens: a temporal, onde estudamos o numero de eventos ao longo do tempo, e a espacial, onde consideramos a localização geográfica dos eventos. Utilizamos uma modelagem estatística baseada em processos pontuais e técnicas de ondaletas para estimar a intensidade temporal ou espacial, isto é, o numero esperado de eventos por unidade de área (na abordagem espacial) ou tempo (na abordagem temporal). Fatores como sexo, faixa etária e tipo de evento (acidentes ou agressões) também foram considerados na análise. Na análise temporal, os resultados indicam que o número esperado de ocorrências em homens é significantemente maior do que em mulheres ao longo do período de observação. O mesmo ocorre com o numero esperado de acidentes quando comparado com o de agressões. As faixas etárias que compreendem as idades de 0 a 14 anos, 15 a 29 anos, 30 a 59 anos e 60 anos ou mais também apresentam números esperados de casos significantemente diferentes entre si. Na análise espacial, escolhemos uma região do Município de São Paulo, nas proximidades do Hospital Saboya, e elaboramos mapas onde é possível identificar geograficamente os locais onde as ocorrências são mais frequentes. A intensidade estimada para o total de eventos indica uma distribuição espacial não homogênea, com grande concentração de eventos principalmente nos distritos do Jabaquara e Cidade Ademar, além de valores altos ao longo das avenidas Bandeirantes, Jabaquara e Cupecê. As intensidades espaciais relativas às agressões a homens e a mulheres, separadamente, apresentam distribuições não homogêneas. Os locais com maiores riscos de agressões a mulheres parecem estar localizados em regiões mais afastadas das grandes avenidas da região. Quando consideramos os acidentes de trânsito e de transporte para cada dia da semana, a análise indicou uma distribuição espacial e temporal heterogênea, com intensidades estimadas maiores nos fins de semana e menores na segunda e terça-feira
We consider a data set with information on victims that were assisted at the emergency room of the Dr. Arthur Ribeiro de Saboya Municipal Hospital, S~ao Paulo, Brazil, from January 1, 2002 to January 11, 2003. We analyze the data chronologically (number of events along time) and spatially (geographical location). The statistical modelling is based on point processes and wavelet techniques to estimate both temporal and spatial intensities, that is, the expected numbers of events by unit time or unit area. The results indicate that the expected number of events is greater for men than for women along the whole observation period. The same is true for the expected number of accidents and that of aggressions, the former being consistently greater than the latter. The expected numbers of events for different age groups (0 to 14, 15 to 29, 30 to 59 and 60 or more) are significantly different. A neighborhood of Saboya Hospital was considered for spatial analysis, according to which it is possible to identify regions where occurrences are most frequent. The spatial distribution of the number of events is non homogeneous with high concentration mostly on Jabaquara and Cidade Ademar districts and along some big avenues (Bandeirantes, Jabaquara and Cupec^e avenues). Spatial non homogeneity of intensities is also observed for both aggressions to men and to women. The regions with the highest risks of aggression to women seam to be located away from the big avenues. When considering traffic and transport accidents separately by each day of the week, the analysis has shown both time and spatial non homogeneous distributions of events with highest estimated intensities during weekends and lowest ones on Monday and Tuesday

CoordenaÃÃo de AperfeÃoamento de Pessoal de NÃvel Superior
Dunas costeiras exercem um importante papel na manutenÃÃo do fluxo de sedimentos da zona costeira. O Parque Nacional de Jericoacoara, localizado no estado do CearÃ, regiÃo Nordeste do Brasil, possui uma morfologia pouco frequente, trata-se de um promontÃrio associado com um campo de dunas mÃveis denominadas barcanas, dunas individuais, de grande porte com formato de ferraduras que se deslocam em direÃÃo L â O. Elas realizam o by-pass, o transporte de sedimentos, essencial para a manutenÃÃo da linha de costa. Neste trabalho, foi priorizada a definiÃÃo da evoluÃÃo morfodinÃmica de dunas mÃveis isoladas (dunas Papai Noel, PÃr-do-Sol e Arraia), tendo como referencial teÃrico a anÃlise das paisagens e como procdimento tÃcnico principal a anÃlise espaÃo-temporal do recobrimento de imagens multitemporais dos satÃlites Landsat e Quickbird entre os anos de 1973 a 2014. AtravÃs da comparaÃÃo da distribuiÃÃo espaÃo temporal das morfologias dunares, nesse perÃodo de 41 anos, evidenciaram-se mudanÃas significativas na Ãrea, perÃmetro e deslocamento das dunas. Foi possÃvel constatar a aÃÃo dos fluxos de matÃria e energia vinculados com migraÃÃo continuada direcionada para a faixa de praia (setor de bypassing de sedimentos). A dinÃmica de migraÃÃo das dunas, quando analisadas apÃs as imagens de 2000, evidenciou possibilidades de alteraÃÃes dos aspectos morfolÃgicos influenciados pelo incremento do fluxo turÃstico, quando instituÃdo o PARNA de Jericoacoara. As mudanÃas foram mais significativas, sobretudo, entre os anos de 2001 a 2005, o que pode estar relacionado a uma maior intervenÃÃo humana (fluxo de turistas). A utilizaÃÃo das tÃcnicas de geoprocessamento para o mapeamento da evoluÃÃo morfodinÃmica do campo de dunas do Parque Nacional de Jericoacoara constituiu- se uma ferramenta essencial para a produÃÃo de informaÃÃes que certamente subsidiarÃo a continuidade do planejamento ambiental da referida, que se constitui como uma Unidade de ConservaÃÃo de ProteÃÃo Integral.
Coastal dunes play an important role in the sediment flow of the coastal zone. The unique morphology of the Jericoacoara National Park in the northeastern Brazilian state of Cearà consists of a promontory covered by a mobile dune field consisting of large, horseshoe-shaped dunes known locally as barcanas that migrate from east to west. These dunes are responsible for the by-pass, the transport of sediments essential for the maintenance of the coastline. The present study focused on the morphodynamic evolution of these isolated mobile dunes through the recovery of multitemporal Landsat and Quickbird satellite images from the years between 1975 and 2014. The comparison of the spatio-temporal distribution of the morphology of these dunes over this 41-year period revealed significant shifts in their area, perimeter, and movement. It was possible to confirm that the flow of material and energy were linked to a process of continuous migration in the direction of the beach (sediment bypassing sector). The dynamics of the dune migration in the years following 2000, when the national park was established, indicate possible impacts of the increase in tourism within the area on the morphology of the dunes. The changes were most significant between 2001 and 2005, possibly reflecting a greater influx of tourists and thus more intense anthropogenic impacts. The different geoprocessing techniques applied to the mapping of the morphodynamic evolution of the dune field of the Jericoacoara National Park proved to be an essential tool for the production of information that will guarantee the long-term environmental planning of this integral conservation unit.

Le code neuronal, c'est-à-dire la manière dont les neurones interconnectés peuvent effectuer des opérations complexes, permettant l'adaptation rapide des animaux à leur environnement, reste une question ouverte et un champ de recherche intensif tant en neurosciences expérimentales qu'en neurosciences computationnelles. Les progrès de la biologie moléculaire et de la microscopie ont récemment permis de surveiller l'activité de neurones individuels chez un animal vivant et, dans le cas de petits animaux ne contenant que quelques milliers de neurones, de mesurer l'activité de l'ensemble du système nerveux. Cependant, le cadre mathématique qui permettrait de combler le fossé entre l'activité d'un seul neurone et les propriétés computationnelles émergentes des ensembles neuronaux fait défaut. Dans le manuscrit de thèse, nous présentons un pipeline de traitement statistique séquentiel qui permet d'extraire efficacement et de manière robuste des ensembles neuronaux à partir de l'imagerie calcique de l'activité neuronale. En particulier, nous développons un cadre d'inférence bayésienne basé sur un modèle biologiquement interprétable pour extraire des ensembles neuronaux caractérisés par du bruit, de l'asynchronisme et du recouvrement. L'outil fourni démontre qu'une procédure d'échantillonnage de Gibbs peut estimer efficacement les paramètres statistiques et les variables latentes pour extraire les ensembles neuronaux basés sur un modèle de synchronisation à la fois sur des données synthétiques et sur des données expérimentales allant de stimulations du cortex visuel de la souris et du poisson zèbre à l'activité spontanée de Hydra Vulgaris. La thèse développe également un cadre statistique de processus ponctuel pour quantifier la façon dont les ensembles neuronaux encodent les stimuli évoqués ou les comportements spontanés chez les animaux vivants. Cet outil polyvalent est également utilisé pour l'inférence de la connectivité fonctionnelle de l'activité neuronale ou la procédure de calibration automatique des algorithmes d'inférence de pics appliqués aux enregistrements calciques. Pour que les algorithmes fournis soient largement diffusés dans la communauté des neurobiologistes, les résultats doivent être étayés par des estimations biologiques interprétables, des preuves statistiques, des démonstrations mathématiques rigoureuses et des logiciels en libre accès. Notre implémentation contributive, qui va de l'intensité des pixels aux ensembles neuronaux estimés, identifie également, à partir des schémas d'activation synchrone des ensembles neuronaux, les neurones ayant des rôles spécifiques qui peuvent être utilisés pour prédire, améliorer ou modifier les comportements d'animaux vivants. Le cadre fourni permet de démontrer l'émergence de propriétés collectives à partir de l'enregistrement de signaux individuels extrêmement variables, qui rendent le code neuronal encore insaisissable
The neural code, i.e. how interconnected neurons can perform complex operations, allowing the quick adaptation of animals to their environment, remains an open question and an intensive field of research both in experimental and computational neurosciences. Advances in molecular biology and microscopy have recently made it possible to monitor the activity of individual neurons in living animals and, in the case of small animals containing only a few thousands of neurons, to measure the activity of the entire nervous system. However, the mathematical framework that would bridge the gap between single neuron activity and the emergent computational properties of neuronal ensembles is missing.In the thesis manuscript, we introduce a sequential statistical processing pipeline that efficiently and robustly extracts neuronal ensembles from calcium imagery of neuronal activity. In particular, we develop a Bayesian inference framework based on a biologically interpretable model to extract neuronal ensembles characterized by noise, asynchrony and overlapping. The provided tool demonstrates that a Gibbs sampling routine can efficiently estimate statistical parameters and hidden variables to uncover neuronal ensembles based on synchronization patterns both on synthetic data and on various experimental datasets from mice and zebrafish visual cortex to Hydra Vulgaris. The thesis equally develops a point process statistical framework to quantify how neuronal ensembles encode evoked stimuli or spontaneous behaviors in living animals. This versatile tool is also used for the inference of the functional connectivity of neuronal activity or the automatically calibration procedure of the spike inference algorithms applied to calcium recordings. For the providing algorithms to be largely spread in the neurobiologist community, results are supported by interpretable biological estimates, statistical evidence, rigorous mathematical proofs, and free-available software. Our contributive implementation, that goes from pixel intensity to estimated neuronal ensembles, equally identify from the synchronous firing patterns of neuronal ensembles, neurons with specific roles that can be used to predict, improve, or alter the behaviors of living animals. The provided framework unravels the emergence of collective properties from the recording of extremely varying individual signals that make the neural code still elusive

In this dissertation, we explore the properties of correlation structure for spatio-temporal point processes and a quantitative spatial process. Spatio-temporal point processes are often assumed to be separable; we propose a formal approach for testing whether a particular data set is indeed separable. Because of the resampling methodology, the approach requires minimal conditions on the underlying spatio-temporal process to perform the hypothesis test, and thus is appropriate for a wide class of models. Africanized Honey Bees (AHBs, Apis mellifera scutellata) abscond more frequently and defend more quickly than colonies of European origin. That they also utilize smaller cavities for building colonies expands their range of suitable hive locations to common objects in urban environments. The aim of the AHB study is to create a model of this quantitative spatial process to predict where AHBs were more likely to build a colony, and to explore what variables might be related to the occurrences of colonies. We constructed two generalized linear models to predict the habitation of water meter boxes, based on surrounding landscape classifications, whether there were colonies in surrounding areas, and other variables. The presence of colonies in the area was a strong predictor of whether AHBs occupied a water meter box, suggesting that AHBs tend to form aggregations, and that the removal of a colony from a water meter box may make other nearby boxes less attractive to the bees.

The modelling and analysis of complex stochastic systems with increasingly large data sets, state-spaces and parameters provides major stimulus to research in Bayesian nonparametric methods and Bayesian computation. This dissertation presents advances in both nonparametric modelling and statistical computation stimulated by challenging problems of analysis in complex spatio-temporal systems and core computational issues in model fitting and model assessment. The first part of the thesis, represented by chapters 2 to 4, concerns novel, nonparametric Bayesian mixture models for spatial point processes, with advances in modelling, computation and applications in biological contexts. Chapter 2 describes and develops models for spatial point processes in which the point outcomes are latent, where indirect observations related to the point outcomes are available, and in which the underlying spatial intensity functions are typically highly heterogenous. Spatial intensities of inhomogeneous Poisson processes are represented via flexible nonparametric Bayesian mixture models. Computational approaches are presented for this new class of spatial point process mixtures and extended to the context of unobserved point process outcomes. Two examples drawn from a central, motivating context, that of immunofluorescence histology analysis in biological studies generating high-resolution imaging data, demonstrate the modelling approach and computational methodology. Chapters 3 and 4 extend this framework to define a class of flexible Bayesian nonparametric models for inhomogeneous spatio-temporal point processes, adding dynamic models for underlying intensity patterns. Dependent Dirichlet process mixture models are introduced as core components of this new time-varying spatial model. Utilizing such nonparametric mixture models for the spatial process intensity functions allows the introduction of time variation via dynamic, state-space models for parameters characterizing the intensities. Bayesian inference and model-fitting is addressed via novel particle filtering ideas and methods. Illustrative simulation examples include studies in problems of extended target tracking and substantive data analysis in cell fluorescent microscopic imaging tracking problems.

The second part of the thesis, consisting of chapters 5 and chapter 6, concerns advances in computational methods for some core and generic Bayesian inferential problems. Chapter 5 develops a novel approach to estimation of upper and lower bounds for marginal likelihoods in Bayesian modelling using refinements of existing variational methods. Traditional variational approaches only provide lower bound estimation; this new lower/upper bound analysis is able to provide accurate and tight bounds in many problems, so facilitates more reliable computation for Bayesian model comparison while also providing a way to assess adequacy of variational densities as approximations to exact, intractable posteriors. The advances also include demonstration of the significant improvements that may be achieved in marginal likelihood estimation by marginalizing some parameters in the model. A distinct contribution to Bayesian computation is covered in Chapter 6. This concerns a generic framework for designing adaptive MCMC algorithms, emphasizing the adaptive Metropolized independence sampler and an effective adaptation strategy using a family of mixture distribution proposals. This work is coupled with development of a novel adaptive approach to computation in nonparametric modelling with large data sets; here a sequential learning approach is defined that iteratively utilizes smaller data subsets. Under the general framework of importance sampling based marginal likelihood computation, the proposed adaptive Monte Carlo method and sequential learning approach can facilitate improved accuracy in marginal likelihood computation. The approaches are exemplified in studies of both synthetic data examples, and in a real data analysis arising in astro-statistics.

Finally, chapter 7 summarizes the dissertation and discusses possible extensions of the specific modelling and computational innovations, as well as potential future work.

Dissertation

Dissertation submitted in partial fulfilment of the requirements for the degree of Master of Science in Geospatial Technologies
The United States of America is the county in the world that is more prone to tornado occurrence. This fact led many researchers, for the past years, to study and formulate theories about tornado occurrence, and which factors promote tornadogenesis. The theories around tornados are always coupled with an attempt to predict their occurrence, for better disaster alertness, and response, in case they happen. At the country level, the tornado occurrence is highly studied and understood. But the same does not happen for the state level, or county level. In this thesis, it is proposed a statistical model to characterize the occurrence of tornados in a state, given physical (terrain roughness and land-cover types)and demographic properties of its counties. This model also takes into consideration the spatial and temporal dimensions, as well as a space time interaction component. This model was applied for Oklahoma and Texas. The model with the covariates fits Texas‟ tornado occurrence, but for Oklahoma, only the spatio-temporal formulation can be applied. For Texas, the model explains the covariates as being congruent with the low-level inflow hypothesis, with tornados decreasing in zones where natural barriers for the flow can be constituted. Under the Bayesian framework, maps of spatial risk and probability of tornado occurrence for Texas and Oklahoma were computed, that can be used to make predictions in the future.