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This work provides a Bayesian nonparametric modeling framework for spatial point processes to account for the irregular domain over which the resulting point pattern occurs in the model formulation while balancing flexible inference with efficient implementation. We start with models for the spatial Poisson process, which assumes independence among points given the number of occurrences, and progress to models for Hawkes processes over space and space-time that capture the self-triggering behaviors and relax the independence assumption. We develop nonparametric Bayesian modeling approaches for Poisson processes using weighted combinations of structured beta densities to represent the point process intensity function. For a regular spatial domain, i.e., the unit square, the model construction implies a Bernstein-Dirichlet prior for the Poisson process density, which supports flexible inference about point process functionals with theoretical guarantees. The key contribution is two classes of flexible and computationally efficient models for spatial Poisson process intensities over irregular domains. We address the choice or estimation of the number of beta basis densities and develop methods for prior specification. For the spatial Hawkes process, we develop a semi-parametric modeling approach, leveraging its clustering representation defined as the superposition of an immigrant Poisson process and several offspring Poisson clustering processes centered on parent points generated by earlier generations. We apply the model for the Poisson process developed earlier to the latent immigrant Poisson process and complete the hierarchical model for the spatial Hawkes process with parametric formulations for the offspring Poisson processes and a model for the latent branching structure that specifies lineage among points. Finally, we develop a nonparametric model for the spatial offspring Poisson process under the assumption of spatial isotropy, which reduces modeling for th

This dissertation builds a modeling framework for non-Gaussian spatial processes, time series, and point processes, with a Bayesian inference paradigm that provides uncertainty quantification. Our methodological development emphasizes direct modeling of non-Gaussianity, in contrast with traditional approaches that consider data transformations or modeling through functionals of the data probability distribution. We achieve the goal by defining a joint distribution through factorization into a product of univariate conditional distributions according to a directed acyclic graph which implies conditional independence. We model each conditional distribution as a weighted combination of first-order conditionals, with weights that can be locally adaptive, for each one of a given number of parents which correspond to spatial nearest-neighbors or temporal lags. Such a formulation features specification of bivariate distributions that define the first-order conditionals for flexible, parsimonious modeling of multivariate non-Gaussian distributions. We obtain, in time, high-order Markov models with stationary marginals, and point process models for limited memory, dependent renewals, and duration clustering; and in space, nearest-neighbor mixture models for spatial processes. Regarding computation, representing the framework by directed acyclic graphs, with a mixture model formulation for the conditionals, gains efficiency and scalability relative to many non-Gaussian models. We develop Markov chain Monte Carlo algorithms for implementation of posterior inference and prediction, with data illustrations in biological, environmental, and social sciences.

We propose a Bayesian nonparametric modeling and inference framework for Hawkes processes. The objective is to increase the inferential scope for this practically important class of point processes by exploring flexible models for its conditional intensity function.As a building block for conditional intensity models, we develop a prior probability model for temporal Poisson process intensities through structured mixtures of Erlang densities with common a scale parameter, mixing on the integer shape parameters. The mixture weights are constructed through increments of a cumulative intensity function modeled nonparametrically with a gamma process prior. This model specification provides a novel extension of Erlang mixtures for density estimation to the intensity estimation setting. Turning to the main dissertation component, we develop different types of nonparametric prior models for the Hawkes process immigrant intensity and for the excitation function (or its normalized version, the offspring density), the two functions that define the point process conditional intensity. The prior models are carefully constructed such that, along with the Hawkes process branching structure, they enable efficient handling of the complex likelihood normalizing terms in implementation of inference. The methodology is further elaborated to construct a flexible and computationally efficient model for marked Hawkes processes. The motivating application involves earthquake data modeling, where the mark is given by the earthquake magnitude. The proposed model builds from a prior for the excitation function that allows flexible shapes for mark-dependent offspring densities. In the context of our motivating application, the modeling approach enables estimation of aftershock densities that can vary with the magnitude of the main shock, unlike existing marked Hawkes process models for earthquake occurrences. For all proposed models, we develop approaches to prior specification and design pos

We propose a Bayesian nonparametric modeling and inference framework for Hawkes processes. The objective is to increase the inferential scope for this practically important class of point processes by exploring flexible models for its conditional intensity function.As a building block for conditional intensity models, we develop a prior probability model for temporal Poisson process intensities through structured mixtures of Erlang densities with common a scale parameter, mixing on the integer shape parameters. The mixture weights are constructed through increments of a cumulative intensity function modeled nonparametrically with a gamma process prior. This model specification provides a novel extension of Erlang mixtures for density estimation to the intensity estimation setting. Turning to the main dissertation component, we develop different types of nonparametric prior models for the Hawkes process immigrant intensity and for the excitation function (or its normalized version, the offspring density), the two functions that define the point process conditional intensity. The prior models are carefully constructed such that, along with the Hawkes process branching structure, they enable efficient handling of the complex likelihood normalizing terms in implementation of inference. The methodology is further elaborated to construct a flexible and computationally efficient model for marked Hawkes processes. The motivating application involves earthquake data modeling, where the mark is given by the earthquake magnitude. The proposed model builds from a prior for the excitation function that allows flexible shapes for mark-dependent offspring densities. In the context of our motivating application, the modeling approach enables estimation of aftershock densities that can vary with the magnitude of the main shock, unlike existing marked Hawkes process models for earthquake occurrences. For all proposed models, we develop approaches to prior specification and design pos

Special education has been a major topic of discussion in all countries of the European Union. Initially, the lack of efforts to establish a system for the protection of the rights of people with disabilities in education received international attention already in the 1980s. The continuation of the efforts was made at the level of the European Union, helping to present the first signs of an institutional national foundation of the rights of the people with special needs. In Greece, society and the legislator proved to be unprepared. Social inclusion and school acceptance of pupils with disabilities was inadequate. In contrast, in the Scandinavian countries the phenomenon of solidarity and welfare is more pronounced. In conclusion, the signs of improving the Greek legislative framework, developing a major political conscience and social "de-stereotyping" are encouraging.

Special education has been a major topic of discussion in all countries of the European Union. Initially, the lack of efforts to establish a system for the protection of the rights of people with disabilities in education received international attention already in the 1980s. The continuation of the efforts was made at the level of the European Union, helping to present the first signs of an institutional national foundation of the rights of the people with special needs. In Greece, society and the legislator proved to be unprepared. Social inclusion and school acceptance of pupils with disabilities was inadequate. In contrast, in the Scandinavian countries the phenomenon of solidarity and welfare is more pronounced. In conclusion, the signs of improving the Greek legislative framework, developing a major political conscience and social "de-stereotyping" are encouraging.

Nonlinearity and high-order auto-dependence are common traits of univariate time series tracking successive states from multidimensional systems. Standard statistical models based on linear stochastic processes are often inadequate to capture these complex dynamics. This work contributes Bayesian statistical methodology and modeling strategies to estimate Markovian transition distributions, particularly when these distributions exhibit non-Gaussianity and/or nonlinear dependence on multiple lags. Given the challenge of modeling high-order nonlinear dynamics, we place emphasis on detecting and exploiting low-order dependence.We propose models for both discrete and continuous state spaces with a common theme of mixture modeling. We first utilize mixtures for soft model selection. To this end, we develop two prior distributions for probability vectors which, in contrast to the popular Dirichlet distribution, retain sparsity properties in the presence of data. Both priors are tractable, allowing for efficient posterior sampling and marginalization. We derive the priors, demonstrate their properties, and employ them for lag selection in the mixture transition distribution model.We then extend the model for estimation and selection in higher-order, discrete-state Markov chains with two primary objectives: parsimonious approximation of high-order dynamics by mixing transition models of lower order, and model selection through over-specification and shrinkage with the new priors to an identifiable and interpretable parameterization. We also extend a continuous-state version of the mixture transition distribution model by admitting nonlinear dependence in the component distributions using Gaussian process priors. We discuss properties of the models and demonstrate their utility with simulation studies and applications to medical, geological, and ecological time series.Finally, we propose and illustrate a Bayesian nonparametric autoregressive mixture model applied to flexibly

Scope of this thesis is the integration and implementation of a collaborative robot in the production line. In the first chapter, the project is described, and its objectives, purpose, boundaries and requirements are defined. Moreover, the project management tools and techniques are presented. All the steps and procedures followed before the initiation of the project are analysed. In the second chapter, the basic theoretical background necessary for a better understanding of the content of this thesis is presented. The history and development of collaborative robots, as well as the industrial evolutions are mentioned. The different types of collaborative robots and their importance in Industry 4.0 and current production are analysed. The third chapter deals with the detailed description of the project. All the devices and equipment are presented thoroughly. The programming logic and working flow is explained. In the last chapter according to the initial objectives, boundaries and requirements the success of the project is assessed. An analysis of how the installation of automate corrugate loader affected the production process is performed. Future changes, improvements and technical suggestions are discussed. The ultimate goal of this thesis project is that the content in the thesis report will be used as a guide for future installations of same or similar type of robots. The aim is to avoid many of the mistakes made, due to rush decisions, lack of experience and communication between team members. The leaning curve obtained during the implementation of the project, can lead to more effective projects in the future., Fokus för denna avhandling är integrering och implementering av en interaktiv robot i en produktionslina. I det första kapitlet beskrivs projektet, och dess mål, syfte, gränser samt krav definieras. Dessutom presenteras verktyg och tekniker för projektledning. Alla de steg och procedurer som använts/följts innan projektet påbörjades har analyserats. I det andra kapitlet presenteras den grundläggande teoretiska bakgrunden för att ge en bättre förståelse av innehållet i denna avhandling. Historien och utvecklingen av interaktiva robotar, liksom de industriella evolutionerna nämns. De olika typerna av interaktiva robotar och deras betydelse i Industri 4.0 och nuvarande produktion analyseras. Det tredje kapitlet innehåller en detaljerad beskrivning av projektet. Alla enheter och utrustning presenteras noggrant. Programmeringslogiken och arbetsflödet förklaras. I det sista kapitlet utvärderas projektets framgång utfrån de ursprungliga målen, gränserna och kraven. En analys utförs av hur installationen av den automatiska laddaren för veckmaskinen påverkar produktionsprocessen. Framtida ändringar, förbättringar och tekniska förslag diskuteras. Det slutliga målet för detta exjobbsarbete är att innehållet i avhandlingen ska användas som en vägledning för framtida installationer av samma eller liknande typ av robotar. Syftet är att undvika många av de misstag som gjorts, på grund av brådska beslut, brist på erfarenhet och kommunikation mellan lagmedlemmar. Lärandekurvan som uppnåtts under genomförandet av projektet kan leda till effektivare projekt i framtiden.

Nonlinearity and high-order auto-dependence are common traits of univariate time series tracking successive states from multidimensional systems. Standard statistical models based on linear stochastic processes are often inadequate to capture these complex dynamics. This work contributes Bayesian statistical methodology and modeling strategies to estimate Markovian transition distributions, particularly when these distributions exhibit non-Gaussianity and/or nonlinear dependence on multiple lags. Given the challenge of modeling high-order nonlinear dynamics, we place emphasis on detecting and exploiting low-order dependence.We propose models for both discrete and continuous state spaces with a common theme of mixture modeling. We first utilize mixtures for soft model selection. To this end, we develop two prior distributions for probability vectors which, in contrast to the popular Dirichlet distribution, retain sparsity properties in the presence of data. Both priors are tractable, allowing for efficient posterior sampling and marginalization. We derive the priors, demonstrate their properties, and employ them for lag selection in the mixture transition distribution model.We then extend the model for estimation and selection in higher-order, discrete-state Markov chains with two primary objectives: parsimonious approximation of high-order dynamics by mixing transition models of lower order, and model selection through over-specification and shrinkage with the new priors to an identifiable and interpretable parameterization. We also extend a continuous-state version of the mixture transition distribution model by admitting nonlinear dependence in the component distributions using Gaussian process priors. We discuss properties of the models and demonstrate their utility with simulation studies and applications to medical, geological, and ecological time series.Finally, we propose and illustrate a Bayesian nonparametric autoregressive mixture model applied to flexibly

Scope of this thesis is the integration and implementation of a collaborative robot in the production line. In the first chapter, the project is described, and its objectives, purpose, boundaries and requirements are defined. Moreover, the project management tools and techniques are presented. All the steps and procedures followed before the initiation of the project are analysed. In the second chapter, the basic theoretical background necessary for a better understanding of the content of this thesis is presented. The history and development of collaborative robots, as well as the industrial evolutions are mentioned. The different types of collaborative robots and their importance in Industry 4.0 and current production are analysed. The third chapter deals with the detailed description of the project. All the devices and equipment are presented thoroughly. The programming logic and working flow is explained. In the last chapter according to the initial objectives, boundaries and requirements the success of the project is assessed. An analysis of how the installation of automate corrugate loader affected the production process is performed. Future changes, improvements and technical suggestions are discussed. The ultimate goal of this thesis project is that the content in the thesis report will be used as a guide for future installations of same or similar type of robots. The aim is to avoid many of the mistakes made, due to rush decisions, lack of experience and communication between team members. The leaning curve obtained during the implementation of the project, can lead to more effective projects in the future., Fokus för denna avhandling är integrering och implementering av en interaktiv robot i en produktionslina. I det första kapitlet beskrivs projektet, och dess mål, syfte, gränser samt krav definieras. Dessutom presenteras verktyg och tekniker för projektledning. Alla de steg och procedurer som använts/följts innan projektet påbörjades har analyserats. I det andra kapitlet presenteras den grundläggande teoretiska bakgrunden för att ge en bättre förståelse av innehållet i denna avhandling. Historien och utvecklingen av interaktiva robotar, liksom de industriella evolutionerna nämns. De olika typerna av interaktiva robotar och deras betydelse i Industri 4.0 och nuvarande produktion analyseras. Det tredje kapitlet innehåller en detaljerad beskrivning av projektet. Alla enheter och utrustning presenteras noggrant. Programmeringslogiken och arbetsflödet förklaras. I det sista kapitlet utvärderas projektets framgång utfrån de ursprungliga målen, gränserna och kraven. En analys utförs av hur installationen av den automatiska laddaren för veckmaskinen påverkar produktionsprocessen. Framtida ändringar, förbättringar och tekniska förslag diskuteras. Det slutliga målet för detta exjobbsarbete är att innehållet i avhandlingen ska användas som en vägledning för framtida installationer av samma eller liknande typ av robotar. Syftet är att undvika många av de misstag som gjorts, på grund av brådska beslut, brist på erfarenhet och kommunikation mellan lagmedlemmar. Lärandekurvan som uppnåtts under genomförandet av projektet kan leda till effektivare projekt i framtiden.

In situ measurements using unmanned aerial vehicles (UAVs) and remote sensing observations can independently provide dense vertically resolved measurements of atmospheric aerosols, information which is strongly required in climate models. In both cases, inverting the recorded signals to useful information requires assumptions and constraints, and this can make the comparison of the results difficult. Here we compare, for the first time, vertical profiles of the aerosol mass concentration derived from light detection and ranging (lidar) observations and in situ measurements using an optical particle counter on board a UAV during moderate and weak Saharan dust episodes. Agreement between the two measurement methods was within experimental uncertainty for the coarse mode (i.e. particles having radii > 0.5ĝ€μm), where the properties of dust particles can be assumed with good accuracy. This result proves that the two techniques can be used interchangeably for determining the vertical profiles of aerosol concentrations, bringing them a step closer towards their systematic exploitation in climate models., Atmospheric Remote Sensing, Geoscience and Remote Sensing

We develop a Bayesian nonparametric framework for modeling ordinal regression relationships which evolve in discrete time. The motivating application involves a key problem in fisheries research on estimating dynamically evolving relationships between age, length and maturity, the latter recorded on an ordinal scale. The methodology builds from nonparametric mixture modeling for the joint stochastic mechanism of covariates and latent continuous responses. This approach yields highly flexible inference for ordinal regression functions while at the same time avoiding the computational challenges of parametric models. A novel dependent Dirichlet process prior for time-dependent mixing distributions extends the model to the dynamic setting. The methodology is used for a detailed study of relationships between maturity, age, and length for Chilipepper rockfish, using data collected over 15 years along the coast of California.

By means of available ice nucleating particle (INP) parameterization schemes we compute profiles of dust INP number concentration utilizing Polly-XT and CALIPSO lidar observations during the INUIT-BACCHUS-ACTRIS 2016 campaign. The polarization-lidar photometer networking (POLIPHON) method is used to separate dust and non-dust aerosol backscatter, extinction, mass concentration, particle number concentration (for particles with radius > 250 nm) and surface area concentration. The INP final products are compared with aerosol samples collected from unmanned aircraft systems (UAS) and analyzed using the ice nucleus counter FRIDGE., Atmospheric Remote Sensing

Aerosol absorption profiling is crucial for radiative transfer calculations and climate modelling. Here, we utilize the synergy of lidar with sun-photometer measurements to derive the absorption coefficient and single scattering albedo profiles during the ACTRIS-2 campaigns held in Germany, Greece and Cyprus. The remote sensing techniques are compared with in situ measurements in order to harmonize and validate the different methodologies and reduce the absorption profiling uncertainties., Atmospheric Remote Sensing

The Cloud-Aerosol Transport System (CATS) onboard the International Space Station (ISS), is a lidar system providing vertically resolved aerosol and cloud profiles since February 2015. In this study, the CATS aerosol product is validated against the aerosol profiles provided by the European Aerosol Research Lidar Network (EARLINET). This validation activity is based on collocated CATS-EARLINET measurements and the comparison of the particle backscatter coefficient at 1064nm., Atmospheric Remote Sensing

We develop a Bayesian nonparametric framework for modeling ordinal regression relationships which evolve in discrete time. The motivating application involves a key problem in fisheries research on estimating dynamically evolving relationships between age, length and maturity, the latter recorded on an ordinal scale. The methodology builds from nonparametric mixture modeling for the joint stochastic mechanism of covariates and latent continuous responses. This approach yields highly flexible inference for ordinal regression functions while at the same time avoiding the computational challenges of parametric models. A novel dependent Dirichlet process prior for time-dependent mixing distributions extends the model to the dynamic setting. The methodology is used for a detailed study of relationships between maturity, age, and length for Chilipepper rockfish, using data collected over 15 years along the coast of California.

The Cloud-Aerosol Transport System (CATS) onboard the International Space Station (ISS), is a lidar system providing vertically resolved aerosol and cloud profiles since February 2015. In this study, the CATS aerosol product is validated against the aerosol profiles provided by the European Aerosol Research Lidar Network (EARLINET). This validation activity is based on collocated CATS-EARLINET measurements and the comparison of the particle backscatter coefficient at 1064nm., Peer Reviewed, Postprint (published version)

By means of available ice nucleating particle (INP) parameterization schemes we compute profiles of dust INP number concentration utilizing Polly-XT and CALIPSO lidar observations during the INUIT-BACCHUS-ACTRIS 2016 campaign. The polarization-lidar photometer networking (POLIPHON) method is used to separate dust and non-dust aerosol backscatter, extinction, mass concentration, particle number concentration (for particles with radius > 250 nm) and surface area concentration. The INP final products are compared with aerosol samples collected from unmanned aircraft systems (UAS) and analyzed using the ice nucleus counter FRIDGE.

The Cloud-Aerosol Transport System (CATS) onboard the International Space Station (ISS), is a lidar system providing vertically resolved aerosol and cloud profiles since February 2015. In this study, the CATS aerosol product is validated against the aerosol profiles provided by the European Aerosol Research Lidar Network (EARLINET). This validation activity is based on collocated CATS-EARLINET measurements and the comparison of the particle backscatter coefficient at 1064nm., Atmospheric Remote Sensing

Aerosol absorption profiling is crucial for radiative transfer calculations and climate modelling. Here, we utilize the synergy of lidar with sun-photometer measurements to derive the absorption coefficient and single scattering albedo profiles during the ACTRIS-2 campaigns held in Germany, Greece and Cyprus. The remote sensing techniques are compared with in situ measurements in order to harmonize and validate the different methodologies and reduce the absorption profiling uncertainties., Atmospheric Remote Sensing

By means of available ice nucleating particle (INP) parameterization schemes we compute profiles of dust INP number concentration utilizing Polly-XT and CALIPSO lidar observations during the INUIT-BACCHUS-ACTRIS 2016 campaign. The polarization-lidar photometer networking (POLIPHON) method is used to separate dust and non-dust aerosol backscatter, extinction, mass concentration, particle number concentration (for particles with radius > 250 nm) and surface area concentration. The INP final products are compared with aerosol samples collected from unmanned aircraft systems (UAS) and analyzed using the ice nucleus counter FRIDGE., Atmospheric Remote Sensing

Stationary time series models built from parametric distributions are, in general, limited in scope due to the assumptions imposed on the residual distribution and autoregression relationship. We present a modeling approach for univariate time series data, which makes no assumptions of stationarity, and can accommodate complex dynamics and capture nonstandard distributions. The model for the transition density arises from the conditional distribution implied by a Bayesian nonparametric mixture of bivariate normals. This implies a flexible autoregressive form for the conditional transition density, defining a time-homogeneous, nonstationary, Markovian model for real-valued data indexed in discrete-time. To obtain a more computationally tractable algorithm for posterior inference, we utilize a square-root-free Cholesky decomposition of the mixture kernel covariance matrix. Results from simulated data suggest the model is able to recover challenging transition and predictive densities. We also illustrate the model on time intervals between eruptions of the Old Faithful geyser. Extensions to accommodate higher order structure and to develop a state-space model are also discussed.

The focus of this work is to develop a Bayesian framework to combine information from multiple parts of the response distribution characterized with different quantiles. The goal is to obtain a synthesized estimate of the covariate effects on the response variable as well as to identify the more influential predictors. This framework naturally relates to the traditional quantile regression, which studies the relationship between the covariates and the conditional quantile of the response variable and serves as an attractive alternative to the more widely used mean regression methods. We achieve the objectives through constructing a Bayesian mixture model using quantile regressions as the mixture components.The first stage of the research involves the development of a parametric family of distributions to provide the mixture kernel for the Bayesian quantile mixture regression. We derive a new family of error distributions for model-based quantile regression called generalized asymmetric Laplace distribution, which is constructed through a structured mixture of normal distributions. The construction enables fixing specific percentiles of the distribution while, at the same time, allowing for varying mode, skewness and tail behavior. This family provides a practically important extension of the asymmetric Laplace distribution, which is the standard error distribution for parametric quantile regression. We develop a Bayesian formulation for the proposed quantile regression model, including conditional lasso regularized quantile regression based on a hierarchical Laplace prior for the regression coefficients, and a Tobit quantile regression model.Next, we develop the main framework to model the conditional distribution of the response with a weighted mixture of quantile regression components. We specify a common regression coefficient vector for all components to synthesize information from multiple parts of the response distribution, each modeled with one quantile regre

We introduce a novel Bayesian modeling approach to spectral density estimation for multiple time series. Considering first the case of non-stationary timeseries, the log-periodogram of each series is modeled as a mixture of Gaussiandistributions with frequency-dependent weights and mean functions. The implied model for the log-spectral density is a mixture of linear mean functionswith frequency-dependent weights. The mixture weights are built throughsuccessive differences of a logit-normal distribution function with frequency-dependent parameters. Building from the construction for a single log-spectraldensity, we develop a hierarchical extension for multiple stationary time series.Specifically, we set the mean functions to be common to all log-spectral densities and model time series specific mixtures through the parameters of thelogit-normal distribution. In addition to accommodating flexible spectral density shapes, a practically important feature of the proposed formulation isthat it allows for ready posterior simulation through a Gibbs sampler withclosed form full conditional distributions for all model parameters. We thenextend the model to multiple locally stationary time series, a particular class of non-stationary time series, making it suitable for the analysis of time series with spectral characteristics that vary slowly with time. The modelingapproach is illustrated with different types of simulated datasets, and used forspectral analysis of multichannel electroencephalographic recordings (EEGs),which provides a key motivating application for the proposed methodology.

The focus of this work is to develop a Bayesian framework to combine information from multiple parts of the response distribution characterized with different quantiles. The goal is to obtain a synthesized estimate of the covariate effects on the response variable as well as to identify the more influential predictors. This framework naturally relates to the traditional quantile regression, which studies the relationship between the covariates and the conditional quantile of the response variable and serves as an attractive alternative to the more widely used mean regression methods. We achieve the objectives through constructing a Bayesian mixture model using quantile regressions as the mixture components.The first stage of the research involves the development of a parametric family of distributions to provide the mixture kernel for the Bayesian quantile mixture regression. We derive a new family of error distributions for model-based quantile regression called generalized asymmetric Laplace distribution, which is constructed through a structured mixture of normal distributions. The construction enables fixing specific percentiles of the distribution while, at the same time, allowing for varying mode, skewness and tail behavior. This family provides a practically important extension of the asymmetric Laplace distribution, which is the standard error distribution for parametric quantile regression. We develop a Bayesian formulation for the proposed quantile regression model, including conditional lasso regularized quantile regression based on a hierarchical Laplace prior for the regression coefficients, and a Tobit quantile regression model.Next, we develop the main framework to model the conditional distribution of the response with a weighted mixture of quantile regression components. We specify a common regression coefficient vector for all components to synthesize information from multiple parts of the response distribution, each modeled with one quantile regre

We introduce a novel Bayesian modeling approach to spectral density estimation for multiple time series. Considering first the case of non-stationary timeseries, the log-periodogram of each series is modeled as a mixture of Gaussiandistributions with frequency-dependent weights and mean functions. The implied model for the log-spectral density is a mixture of linear mean functionswith frequency-dependent weights. The mixture weights are built throughsuccessive differences of a logit-normal distribution function with frequency-dependent parameters. Building from the construction for a single log-spectraldensity, we develop a hierarchical extension for multiple stationary time series.Specifically, we set the mean functions to be common to all log-spectral densities and model time series specific mixtures through the parameters of thelogit-normal distribution. In addition to accommodating flexible spectral density shapes, a practically important feature of the proposed formulation isthat it allows for ready posterior simulation through a Gibbs sampler withclosed form full conditional distributions for all model parameters. We thenextend the model to multiple locally stationary time series, a particular class of non-stationary time series, making it suitable for the analysis of time series with spectral characteristics that vary slowly with time. The modelingapproach is illustrated with different types of simulated datasets, and used forspectral analysis of multichannel electroencephalographic recordings (EEGs),which provides a key motivating application for the proposed methodology.

Stationary time series models built from parametric distributions are, in general, limited in scope due to the assumptions imposed on the residual distribution and autoregression relationship. We present a modeling approach for univariate time series data, which makes no assumptions of stationarity, and can accommodate complex dynamics and capture nonstandard distributions. The model for the transition density arises from the conditional distribution implied by a Bayesian nonparametric mixture of bivariate normals. This implies a flexible autoregressive form for the conditional transition density, defining a time-homogeneous, nonstationary, Markovian model for real-valued data indexed in discrete-time. To obtain a more computationally tractable algorithm for posterior inference, we utilize a square-root-free Cholesky decomposition of the mixture kernel covariance matrix. Results from simulated data suggest the model is able to recover challenging transition and predictive densities. We also illustrate the model on time intervals between eruptions of the Old Faithful geyser. Extensions to accommodate higher order structure and to develop a state-space model are also discussed.

We propose a general nonparametric Bayesian framework for binary regression, which is built from modeling for the joint response-covariate distribution. The observed binary responses are assumed to arise from underlying continuous random variables through discretization, and we model the joint distribution of these latent responses and the covariates using a Dirichlet process mixture of multivariate normals. We show that the kernel of the induced mixture model for the observed data is identifiable upon a restriction on the latent variables. To allow for appropriate dependence structure while facilitating identifiability, we use a square-root-free Cholesky decomposition of the covariance matrix in the normal mixture kernel. In addition to allowing for the necessary restriction, this modeling strategy provides substantial simplifications in implementation of Markov chain Monte Carlo posterior simulation. We present two data examples taken from areas for which the methodology is especially well suited. In particular, the first example involves estimation of relationships between environmental variables, and the second develops inference for natural selection surfaces in evolutionary biology. Finally, we discuss extensions to regression settings with ordinal responses.

Seasonal point processes refer to stochastic models for random events which are only observed in a given season. We develop nonparametric Bayesian methodology to study the dynamic evolution of a seasonal marked point process intensity. We assume the point process is a nonhomogeneous Poisson process and propose a nonparametric mixture of beta densities to model dynamically evolving temporal Poisson process intensities. Dependence structure is built through a dependent Dirichlet process prior for the seasonally-varying mixing distributions.We extend the nonparametric model to incorporate time-varying marks, resulting in flexible inference for both the seasonal point process intensity and for the conditional mark distribution. The motivating application involves the analysis of hurricane landfalls with reported damages along the U.S. Gulf and Atlantic coasts from 1900 to 2010. We focus on studying the evolution of the intensity of the process of hurricane landfall occurrences, and the respective maximum wind speed and associated damages. Our results indicate an increase in the number of hurricane landfall occurrences and a decrease in the median maximum wind speed at the peak of the season. Introducing standardized damage as a mark, such that reported damages are comparable both in time and space, we find that there is no significant rising trend in hurricane damages over time.

Model-based inferential methods for point processes have received less attention than the corresponding theory of point processes and is more scarcely developed than other areas of statistical inference.Classical inferential methods for point processes include likelihood-based and nonparametric methods. Bayesian analysis provides simulation-based estimation of several statistics of interest for point processes. However, a challenge of Bayesian modeling, specifically for point processes, is selecting an appropriate parametric form for the intensity function. Bayesian nonparametric methods aim to avoid the narrow focus of parametric assumptions by imposing priors that can support the entire space of distributions and functions. It is naturally a more flexible and adaptable approach than those based on parametric models. In this dissertation, we focus on developing methodology for some classes of temporal point processes modeling and inference in the context of Bayesian nonparametric methods, mainly with applications in environmental science. Firstly, we are motivated to study seasonal marked point process by an application of hurricanes occurrences. We develop nonparametric Bayesian methodology to study the dynamic evolution of a seasonal marked point process intensity under the assumption that the point process is a non-homogeneous Poisson process. The dynamic model for time-varying intensities provides both the intra-seasonal and inter-seasonal variability of occurrences of events. Considering marks, we provide a full probabilistic model for the point process over the joint marks-points space which allows for different types of inferences, including full inference for dynamically evolving conditional mark densities given a time point, a particular time period, and even a subset of marks. We apply this method to study the evolution of the intensity of the process of hurricane landfall occurrences, and the respective maximum wind speed and associated damages. We show

Integro-Differential Equations (IDEs) are a novel way of dynamically modeling spatio-temporal data. IDEs are characterized by a kernel which controls the spatial and temporal associations. The ubiquitous choice for kernel has been Gaussian. We explore advantages of more flexible kernel choices. One-dimensional space is considered initially, replacing the Gaussian IDE kernel with more flexible parametric families of distributions. The kernels are chosen based on stochastic partial differential equation approximations which connect characteristics of the kernel with interpretable physical properties of the underlying process controlling the data. Next, Dirichlet process mixtures of normal distributions are used to model non-parametrically the IDE kernel. Computational issues arise using non-parametric kernels which are solved using Hermite polynomials and Hamiltonian Monte Carlo sampling. To develop flexible modeling in two-dimensional space, we propose bivariate stable distributions as IDE kernels. By using Bernstein polynomials as a prior for the measure defining the bivariate stable, a wide variety of shapes can be achieved. Bivariate stable kernels will be shown to outperform the Gaussian kernel by comparing K-step ahead predictions for Pacific sea surface temperature anomalies. Through study of properties for the proposed models, and empirical investigation with synthetic and real data, we demonstrate that the methodology has the potential to significantly improve the inference and forecasting capacity of IDE models based on Gaussian kernels.

Heart failure is a leading cause of morbidity and mortality in the western world. One of the effects of heart failure is the structural remodelling of cardiac tissue, including tissue dilation and development of fibrosis. It is therefore important to study these changes and their effect on cardiac activity, in order to gain a better understanding of the underlying mechanisms in arrhythmogenesis, which will hopefully enable us to develop better treatments for heart failure. In this study we developed biophysically detailed models of the rabbit atria for normal and heart failure conditions. These models were used to study the effects of structural remodelling of heart failure on cardiac excitation wave conduction. Anatomical reconstructions of the control and heart failure hearts were based on contrast enhanced micro-CT imaging. Fibre orientation was extracted from the control and heart failure datasets. Effects of heart failure geometry on the activation pattern of atrial excitation waves were analyzed. It was found that atrial activation time increased from the control to the heart failure case in both isotropic and anisotropic conditions, which is attributed primarily to the dilation of tissue caused by heart failure.

Heart failure is a leading cause of morbidity and mortality in the western world. One of the effects of heart failure is the structural remodelling of cardiac tissue, including tissue dilation and development of fibrosis. It is therefore important to study these changes and their effect on cardiac activity, in order to gain a better understanding of the underlying mechanisms in arrhythmogenesis, which will hopefully enable us to develop better treatments for heart failure. In this study we developed biophysically detailed models of the rabbit atria for normal and heart failure conditions. These models were used to study the effects of structural remodelling of heart failure on cardiac excitation wave conduction. Anatomical reconstructions of the control and heart failure hearts were based on contrast enhanced micro-CT imaging. Fibre orientation was extracted from the control and heart failure datasets. Effects of heart failure geometry on the activation pattern of atrial excitation waves were analyzed. It was found that atrial activation time increased from the control to the heart failure case in both isotropic and anisotropic conditions, which is attributed primarily to the dilation of tissue caused by heart failure.

Heart failure is a leading cause of morbidity and mortality in the western world. One of the effects of heart failure is the structural remodelling of cardiac tissue, including tissue dilation and development of fibrosis. It is therefore important to study these changes and their effect on cardiac activity, in order to gain a better understanding of the underlying mechanisms in arrhythmogenesis, which will hopefully enable us to develop better treatments for heart failure. In this study we developed biophysically detailed models of the rabbit atria for normal and heart failure conditions. These models were used to study the effects of structural remodelling of heart failure on cardiac excitation wave conduction. Anatomical reconstructions of the control and heart failure hearts were based on contrast enhanced micro-CT imaging. Fibre orientation was extracted from the control and heart failure datasets. Effects of heart failure geometry on the activation pattern of atrial excitation waves were analyzed. It was found that atrial activation time increased from the control to the heart failure case in both isotropic and anisotropic conditions, which is attributed primarily to the dilation of tissue caused by heart failure.

Model-based inferential methods for point processes have received less attention than the corresponding theory of point processes and is more scarcely developed than other areas of statistical inference.Classical inferential methods for point processes include likelihood-based and nonparametric methods. Bayesian analysis provides simulation-based estimation of several statistics of interest for point processes. However, a challenge of Bayesian modeling, specifically for point processes, is selecting an appropriate parametric form for the intensity function. Bayesian nonparametric methods aim to avoid the narrow focus of parametric assumptions by imposing priors that can support the entire space of distributions and functions. It is naturally a more flexible and adaptable approach than those based on parametric models. In this dissertation, we focus on developing methodology for some classes of temporal point processes modeling and inference in the context of Bayesian nonparametric methods, mainly with applications in environmental science. Firstly, we are motivated to study seasonal marked point process by an application of hurricanes occurrences. We develop nonparametric Bayesian methodology to study the dynamic evolution of a seasonal marked point process intensity under the assumption that the point process is a non-homogeneous Poisson process. The dynamic model for time-varying intensities provides both the intra-seasonal and inter-seasonal variability of occurrences of events. Considering marks, we provide a full probabilistic model for the point process over the joint marks-points space which allows for different types of inferences, including full inference for dynamically evolving conditional mark densities given a time point, a particular time period, and even a subset of marks. We apply this method to study the evolution of the intensity of the process of hurricane landfall occurrences, and the respective maximum wind speed and associated damages. We show

Integro-Differential Equations (IDEs) are a novel way of dynamically modeling spatio-temporal data. IDEs are characterized by a kernel which controls the spatial and temporal associations. The ubiquitous choice for kernel has been Gaussian. We explore advantages of more flexible kernel choices. One-dimensional space is considered initially, replacing the Gaussian IDE kernel with more flexible parametric families of distributions. The kernels are chosen based on stochastic partial differential equation approximations which connect characteristics of the kernel with interpretable physical properties of the underlying process controlling the data. Next, Dirichlet process mixtures of normal distributions are used to model non-parametrically the IDE kernel. Computational issues arise using non-parametric kernels which are solved using Hermite polynomials and Hamiltonian Monte Carlo sampling. To develop flexible modeling in two-dimensional space, we propose bivariate stable distributions as IDE kernels. By using Bernstein polynomials as a prior for the measure defining the bivariate stable, a wide variety of shapes can be achieved. Bivariate stable kernels will be shown to outperform the Gaussian kernel by comparing K-step ahead predictions for Pacific sea surface temperature anomalies. Through study of properties for the proposed models, and empirical investigation with synthetic and real data, we demonstrate that the methodology has the potential to significantly improve the inference and forecasting capacity of IDE models based on Gaussian kernels.

We propose a general nonparametric Bayesian framework for binary regression, which is built from modeling for the joint response-covariate distribution. The observed binary responses are assumed to arise from underlying continuous random variables through discretization, and we model the joint distribution of these latent responses and the covariates using a Dirichlet process mixture of multivariate normals. We show that the kernel of the induced mixture model for the observed data is identifiable upon a restriction on the latent variables. To allow for appropriate dependence structure while facilitating identifiability, we use a square-root-free Cholesky decomposition of the covariance matrix in the normal mixture kernel. In addition to allowing for the necessary restriction, this modeling strategy provides substantial simplifications in implementation of Markov chain Monte Carlo posterior simulation. We present two data examples taken from areas for which the methodology is especially well suited. In particular, the first example involves estimation of relationships between environmental variables, and the second develops inference for natural selection surfaces in evolutionary biology. Finally, we discuss extensions to regression settings with ordinal responses.

Seasonal point processes refer to stochastic models for random events which are only observed in a given season. We develop nonparametric Bayesian methodology to study the dynamic evolution of a seasonal marked point process intensity. We assume the point process is a nonhomogeneous Poisson process and propose a nonparametric mixture of beta densities to model dynamically evolving temporal Poisson process intensities. Dependence structure is built through a dependent Dirichlet process prior for the seasonally-varying mixing distributions.We extend the nonparametric model to incorporate time-varying marks, resulting in flexible inference for both the seasonal point process intensity and for the conditional mark distribution. The motivating application involves the analysis of hurricane landfalls with reported damages along the U.S. Gulf and Atlantic coasts from 1900 to 2010. We focus on studying the evolution of the intensity of the process of hurricane landfall occurrences, and the respective maximum wind speed and associated damages. Our results indicate an increase in the number of hurricane landfall occurrences and a decrease in the median maximum wind speed at the peak of the season. Introducing standardized damage as a mark, such that reported damages are comparable both in time and space, we find that there is no significant rising trend in hurricane damages over time.

Heart failure is a leading cause of morbidity and mortality in the western world. One of the effects of heart failure is the structural remodelling of cardiac tissue, including tissue dilation and development of fibrosis. It is therefore important to study these changes and their effect on cardiac activity, in order to gain a better understanding of the underlying mechanisms in arrhythmogenesis, which will hopefully enable us to develop better treatments for heart failure. In this study we developed biophysically detailed models of the rabbit atria for normal and heart failure conditions. These models were used to study the effects of structural remodelling of heart failure on cardiac excitation wave conduction. Anatomical reconstructions of the control and heart failure hearts were based on contrast enhanced micro-CT imaging. Fibre orientation was extracted from the control and heart failure datasets. Effects of heart failure geometry on the activation pattern of atrial excitation waves were analyzed. It was found that atrial activation time increased from the control to the heart failure case in both isotropic and anisotropic conditions, which is attributed primarily to the dilation of tissue caused by heart failure.

Heart failure is a leading cause of morbidity and mortality in the western world. One of the effects of heart failure is the structural remodelling of cardiac tissue, including tissue dilation and development of fibrosis. It is therefore important to study these changes and their effect on cardiac activity, in order to gain a better understanding of the underlying mechanisms in arrhythmogenesis, which will hopefully enable us to develop better treatments for heart failure. In this study we developed biophysically detailed models of the rabbit atria for normal and heart failure conditions. These models were used to study the effects of structural remodelling of heart failure on cardiac excitation wave conduction. Anatomical reconstructions of the control and heart failure hearts were based on contrast enhanced micro-CT imaging. Fibre orientation was extracted from the control and heart failure datasets. Effects of heart failure geometry on the activation pattern of atrial excitation waves were analyzed. It was found that atrial activation time increased from the control to the heart failure case in both isotropic and anisotropic conditions, which is attributed primarily to the dilation of tissue caused by heart failure.

Heart failure is a leading cause of morbidity and mortality in the western world. One of the effects of heart failure is the structural remodelling of cardiac tissue, including tissue dilation and development of fibrosis. It is therefore important to study these changes and their effect on cardiac activity, in order to gain a better understanding of the underlying mechanisms in arrhythmogenesis, which will hopefully enable us to develop better treatments for heart failure. In this study we developed biophysically detailed models of the rabbit atria for normal and heart failure conditions. These models were used to study the effects of structural remodelling of heart failure on cardiac excitation wave conduction. Anatomical reconstructions of the control and heart failure hearts were based on contrast enhanced micro-CT imaging. Fibre orientation was extracted from the control and heart failure datasets. Effects of heart failure geometry on the activation pattern of atrial excitation waves were analyzed. It was found that atrial activation time increased from the control to the heart failure case in both isotropic and anisotropic conditions, which is attributed primarily to the dilation of tissue caused by heart failure.

We develop a Bayesian nonparametric mixture modeling framework for quantal bioassay settings. The approach is built upon modeling dose-dependent response distributions. We adopt a structured nonparametric prior mixture model, which induces a monotonicity restriction for the dose-response curve. Particular emphasis is placed on the key risk assessment goal of calibration for the dose level that corresponds to a specified response. The proposed methodology yields flexible inference for the dose-response relationship as well as for other inferential objectives, as illustrated with two data sets from the literature.

Traditional approaches to ordinal regression rely on strong parametric assumptions for the regression function and/or the underlying response distribution. While they simplify inference, restrictions such as normality and linearity are inappropriate for most settings, and the need for flexible, nonlinear models which relax common distributional assumptions is clear. Through the use of Bayesian nonparametric modeling techniques, nonstandard features of regression relationships may be obtained if the data suggest them to be present. We introduce a general framework for multivariate ordinal regression, which is not restricted by linearity or additivity assumptions in the covariate effects. In particular, we assume the ordinal responses arise from latent continuous random variables through discretization, and model the latent response-covariate distribution using a Dirichlet process mixture of multivariate normals. We begin with the binary regression setting, both due to its prominent role in the literature and because it requires more specialized model development under our framework. In particular, we use a square-root-free Cholesky decomposition of the normal kernel covariance matrix, which facilitates model identifiability while allowing for appropriate dependence structure. Moreover, this model structure has the computational advantage of simplifying the implementation of Markov Chain Monte Carlo posterior simulation. Next, we develop modeling and inference methods for ordinal regression, including the underdeveloped setting that involves multivariate ordinal responses. Standard parametric models for ordinal regression suffer from computational challenges arising from identifiability constraints and parameter estimation, whereas due to the flexible nature of the nonparametric model, we overcome these difficulties. The modeling approach is further developed to handle ordinal regressions which are indexed in discrete-time, through use of a dependent Dirichlet process

Traditional approaches to ordinal regression rely on strong parametric assumptions for the regression function and/or the underlying response distribution. While they simplify inference, restrictions such as normality and linearity are inappropriate for most settings, and the need for flexible, nonlinear models which relax common distributional assumptions is clear. Through the use of Bayesian nonparametric modeling techniques, nonstandard features of regression relationships may be obtained if the data suggest them to be present. We introduce a general framework for multivariate ordinal regression, which is not restricted by linearity or additivity assumptions in the covariate effects. In particular, we assume the ordinal responses arise from latent continuous random variables through discretization, and model the latent response-covariate distribution using a Dirichlet process mixture of multivariate normals. We begin with the binary regression setting, both due to its prominent role in the literature and because it requires more specialized model development under our framework. In particular, we use a square-root-free Cholesky decomposition of the normal kernel covariance matrix, which facilitates model identifiability while allowing for appropriate dependence structure. Moreover, this model structure has the computational advantage of simplifying the implementation of Markov Chain Monte Carlo posterior simulation. Next, we develop modeling and inference methods for ordinal regression, including the underdeveloped setting that involves multivariate ordinal responses. Standard parametric models for ordinal regression suffer from computational challenges arising from identifiability constraints and parameter estimation, whereas due to the flexible nature of the nonparametric model, we overcome these difficulties. The modeling approach is further developed to handle ordinal regressions which are indexed in discrete-time, through use of a dependent Dirichlet process

We develop a Bayesian nonparametric mixture modeling framework for quantal bioassay settings. The approach is built upon modeling dose-dependent response distributions. We adopt a structured nonparametric prior mixture model, which induces a monotonicity restriction for the dose-response curve. Particular emphasis is placed on the key risk assessment goal of calibration for the dose level that corresponds to a specified response. The proposed methodology yields flexible inference for the dose-response relationship as well as for other inferential objectives, as illustrated with two data sets from the literature.

In survival analysis interest lies in modeling data that describe the time to a particular event. Informative functions, namely the hazard function and mean residual life function, can be obtained from the model's distribution function. We focus on the mean residual life function which provides the expected remaining life given that the subject has survived (i.e., is event-free) up to a particular time. This function is of direct interest in reliability, medical, and actuarial fields. In addition to its practical interpretation, the mean residual life function characterizes the survival distribution. In terms of mean residual life function inference, there are two shortcomings present in the current literature. First off, the shape of the functional is often restricted, which forces the researcher to make an assumption that may not be appropriate. Secondly, in cases where the shape of the functional is not parametrically specified, full inference is not obtained. The aim of our research is to provide a modeling approach that yields full inference for the mean residual life function, and is not restrictive on the shape of the functional. In particular, we develop general Bayesian nonparametric modeling methods for inference for mean residual life functions built from a mixture model for the associated survival distribution. Although the prior model is not placed on the mean residual life function directly, our methods offer rich inference for the desired functional. We place a Dirichlet process mixture model on the survival function, and discuss the importance of careful kernel selection to ensure desirable properties for the mean residual life function. We advocate for a mixture model with a gamma kernel and dependent baseline distribution for the Dirichlet process prior. We extend our model to the regression setting by modeling the joint distribution for the survival response and random covariates. This approach provides a flexible method for obtaining inference fo