Bayesian Networks and Gaussian Mixture Models in Multi-Dimensional Data Analysis with Application to Religion-Conflict Data

abstract: This thesis examines the application of statistical signal processing approaches to data arising from surveys intended to measure psychological and sociological phenomena underpinning human social dynamics. The use of signal processing methods for analysis of signals arising from measurement of social, biological, and other non-traditional phenomena has been an important and growing area of signal processing research over the past decade. Here, we explore the application of statistical modeling and signal processing concepts to data obtained from the Global Group Relations Project, specifically to understand and quantify the effects and interactions of social psychological factors related to intergroup conflicts. We use Bayesian networks to specify prospective models of conditional dependence. Bayesian networks are determined between social psychological factors and conflict variables, and modeled by directed acyclic graphs, while the significant interactions are modeled as conditional probabilities. Since the data are sparse and multi-dimensional, we regress Gaussian mixture models (GMMs) against the data to estimate the conditional probabilities of interest. The parameters of GMMs are estimated using the expectation-maximization (EM) algorithm. However, the EM algorithm may suffer from over-fitting problem due to the high dimensionality and limited observations entailed in this data set. Therefore, the Akaike information criterion (AIC) and the Bayesian information criterion (BIC) are used for GMM order estimation. To assist intuitive understanding of the interactions of social variables and the intergroup conflicts, we introduce a color-based visualization scheme. In this scheme, the intensities of colors are proportional to the conditional probabilities observed.Dissertation/ThesisM.S. Electrical Engineering 201

Isotonic distributional regression

Isotonic distributional regression (IDR) is a powerful non-parametric technique for the estimation of conditional distributions under order restrictions. In a nutshell, IDR learns conditional distributions that are calibrated, and simultaneously optimal relative to comprehensive classes of relevant loss functions, subject to isotonicity constraints in terms of a partial order on the covariate space. Non-parametric isotonic quantile regression and non-parametric isotonic binary regression emerge as special cases. For prediction, we propose an interpolation method that generalizes extant specifications under the pool adjacent violators algorithm. We recommend the use of IDR as a generic benchmark technique in probabilistic forecast problems, as it does not involve any parameter tuning nor implementation choices, except for the selection of a partial order on the covariate space. The method can be combined with subsample aggregation, with the benefits of smoother regression functions and gains in computational efficiency. In a simulation study, we compare methods for distributional regression in terms of the continuous ranked probability score (CRPS) and 2 estimation error, which are closely linked. In a case study on raw and post-processed quantitative precipitation forecasts from a leading numerical weather prediction system, IDR is competitive with state of the art techniques

Isotonic Distributional Regression

Isotonic distributional regression (IDR) is a powerful nonparametric technique for the estimation of conditional distributions under order restrictions. In a nutshell, IDR learns conditional distributions that are calibrated, and simultaneously optimal relative to comprehensive classes of relevant loss functions, subject to isotonicity constraints in terms of a partial order on the covariate space. Nonparametric isotonic quantile regression and nonparametric isotonic binary regression emerge as special cases. For prediction, we propose an interpolation method that generalizes extant specifications under the pool adjacent violators algorithm. We recommend the use of IDR as a generic benchmark technique in probabilistic forecast problems, as it does not involve any parameter tuning nor implementation choices, except for the selection of a partial order on the covariate space. The method can be combined with subsample aggregation, with the benefits of smoother regression functions and gains in computational efficiency. In a simulation study, we compare methods for distributional regression in terms of the continuous ranked probability score (CRPS) and $L_2$ estimation error, which are closely linked. In a case study on raw and postprocessed quantitative precipitation forecasts from a leading numerical weather prediction system, IDR is competitive with state of the art techniques

Machine Learning

Machine Learning can be defined in various ways related to a scientific domain concerned with the design and development of theoretical and implementation tools that allow building systems with some Human Like intelligent behavior. Machine learning addresses more specifically the ability to improve automatically through experience

Advanced source separation methods with applications to spatio-temporal datasets

Latent variable models are useful tools for statistical data analysis in many applications. Examples of popular models include factor analysis, state-space models and independent component analysis. These types of models can be used for solving the source separation problem in which the latent variables should have a meaningful interpretation and represent the actual sources generating data. Source separation methods is the main focus of this work. Bayesian statistical theory provides a principled way to learn latent variable models and therefore to solve the source separation problem. The first part of this work studies variational Bayesian methods and their application to different latent variable models. The properties of variational Bayesian methods are investigated both theoretically and experimentally using linear source separation models. A new nonlinear factor analysis model which restricts the generative mapping to the practically important case of post-nonlinear mixtures is presented. The variational Bayesian approach to learning nonlinear state-space models is studied as well. This method is applied to the practical problem of detecting changes in the dynamics of complex nonlinear processes. The main drawback of Bayesian methods is their high computational burden. This complicates their use for exploratory data analysis in which observed data regularities often suggest what kind of models could be tried. Therefore, the second part of this work proposes several faster source separation algorithms implemented in a common algorithmic framework. The proposed approaches separate the sources by analyzing their spectral contents, decoupling their dynamic models or by optimizing their prominent variance structures. These algorithms are applied to spatio-temporal datasets containing global climate measurements from a long period of time.reviewe

Magistrates' decision-making: personality, process and outcome

The thesis examined personality and socio-demographic characteristics of individuals and their relationship to the way in which magistrates approach the sentencing of offenders and the choices they make. It was based on a review of the theoretical approaches to models of decision-making and the concept of individual differences. A pluralistic methodology was adopted combining a quasi-experimental approach in the first study, with two further qualitative studies. Study 1 reported the profile data for the participants, all practising magistrates, and their responses to case study vignettes. Study 2 considered participants' perception of the sentencing process and the factors that influenced their decisions using an interpretative phenomenological approach, while Study 3 applied content and discourse analysis to transcripts of a sentencing training exercise in which magistrates had participated. Analyses of the first study were mostly correlational. Modest associations between Locus of Control and Legal Authoriarianism with severity of sentence were demonstrated and also small gender differences in sentencing choice. The study concluded that there was no support for hypotheses linking other personality trait measurements with the severity of sentence or the approach adopted, using an algebraic model to represent the process. In the subsequent studies, evidence emerged to suggest a more holistic approach to sentencing, guided by advice on structured decision-making, while accommodating the influences of probation service reports, diverse sentencing aims and the advice of the legal professionals. The impact of group interactions was also apparent. This varied with individual characteristics and acquired competences necessary for satisfactory appraisal. The interpretation of 'roles' on a sentencing Bench and their potential effects on the process and outcome of sentencing was observed

Isotonic Distributional Regression

Distributional regression estimates the probability distribution of a response variable conditional on covariates. The estimated conditional distribution comprehensively summarizes the available information on the response variable, and allows to derive all statistical quantities of interest, such as the conditional mean, threshold exceedance probabilities, or quantiles. This thesis develops isotonic distributional regression, a method for estimating conditional distributions under the assumption of a monotone relationship between covariates and a response variable. The response variable is univariate and real-valued, and the covariates lie in a partially ordered set. The monotone relationship is formulated in terms of stochastic order constraints, that is, the response variable increases in a stochastic sense as the covariates increase in the partial order. This assumption alone yields a shape-constrained non-parametric estimator, which does not involve any tuning parameters. The estimation of distributions under stochastic order restrictions has already been studied for various stochastic orders, but so far only with totally ordered covariates. Apart from considering more general partially ordered covariates, the first main contribution of this thesis lies in a shift of focus from estimation to prediction. Distributional regression is the backbone of probabilistic forecasting, which aims at quantifying the uncertainty about a future quantity of interest comprehensively in the form of probability distributions. When analyzed with respect to predominant criteria for probabilistic forecast quality, isotonic distributional regression is shown to have desirable properties. In addition, this thesis develops an efficient algorithm for the computation of isotonic distributional regression, and proposes an estimator under a weaker, previously not thoroughly studied stochastic order constraint. A main application of isotonic distributional regression is the uncertainty quantification for point forecasts. Such point forecasts sometimes stem from external sources, like physical models or expert surveys, but often they are generated with statistical models. The second contribution of this thesis is the extension of isotonic distributional regression to allow covariates that are point predictions from a regression model, which may be trained on the same data to which isotonic distributional regression is to be applied. This combination yields a so-called distributional index model. Asymptotic consistency is proved under suitable assumptions, and real data applications demonstrate the usefulness of the method. Isotonic distributional regression provides a benchmark in forecasting problems, as it allows to quantify the merits of a specific, tailored model for the application at hand over a generic method which only relies on monotonicity. In such comparisons it is vital to assess the significance of forecast superiority or of forecast misspecification. The third contribution of this thesis is the development of new, safe methods for forecast evaluation, which require no or minimal assumptions on the data generating processes

Measuring child poverty in Lesotho

EThOS - Electronic Theses Online ServiceGBUnited Kingdo

Pattern Recognition

Pattern recognition is a very wide research field. It involves factors as diverse as sensors, feature extraction, pattern classification, decision fusion, applications and others. The signals processed are commonly one, two or three dimensional, the processing is done in real- time or takes hours and days, some systems look for one narrow object class, others search huge databases for entries with at least a small amount of similarity. No single person can claim expertise across the whole field, which develops rapidly, updates its paradigms and comprehends several philosophical approaches. This book reflects this diversity by presenting a selection of recent developments within the area of pattern recognition and related fields. It covers theoretical advances in classification and feature extraction as well as application-oriented works. Authors of these 25 works present and advocate recent achievements of their research related to the field of pattern recognition

The cognitive and personality differences of supernatural belief.

This thesis set out to meet the following aim and objectives: Aim: Examine cognition and personality of people who hold different types of supernatural belief. Objective 1: Create and validate a new scale to measure supernatural belief. Objective 2: Create and test a new model of supernatural belief based on cognition and personality. This would potentially test two hypotheses: the Cognitive Deficits Hypothesis and the Psychodynamics Functions Hypothesis. This was accomplished by conducting four studies. Studies one and two created and validated the new Belief in the Supernatural Scale (BitSS), a 44 item scale with the following five factors: ‘mental and psychic phenomena’, ‘religious belief’, ‘psychokinesis’, ‘supernatural entities’, and ‘common paranormal perceptions’. Cognition and personality would be looked at within the context of four different types of believer: ‘believers’, ‘paranormal believers’, ‘sceptics’ and ‘religious believers’. Study three revealed two profiles relating to cognition: ‘reflective thinkers’ and ‘intuitive believers’. The reflective profile was more likely to contain ‘sceptics’ and ‘believers’, and least likely to contain ‘paranormal believers’. The intuitive group was more likely to contain ‘religious believers’ and ‘believers’. The final study looked at personality alongside cognition and revealed ‘sensitive and abstract thinkers’ and ‘reflective metacognitive dogmatists’ profiles. The ‘sensitive and abstract thinkers’ were least likely to contain ‘sceptics’ and ‘religious believers’ and most likely to contain ‘believers’ and ‘paranormal believers’. The ‘reflective metacognitive dogmatists’ were most likely to contain ‘religious believers’ and ‘believers’ and least likely to contain ‘paranormal believers’. Following this analysis, Structural Equation Modelling was used to test seven different models of personality, cognition and belief. Studies one and two indicated a clear separation of religious and paranormal belief within the new scale, and that spiritual belief overlaps between the two. The scale developed was reliable and valid, and accurately reflected the concept of supernatural belief and enabled the measurement of religious and paranormal belief, where the overlaps were acknowledged whilst still being separate beliefs. Studies three and four found the ‘sceptics’ and ‘religious believers’ have remarkably similar profiles, indicating that the religious beliefs themselves may have been cognitively ring-fenced off in some way. The ‘paranormal believers’ however were not reflective thinkers and were not metacognitively active, indicating that they were not aware that they were not thinking critically or analytically. The Structural Equation Model showed that schizotypy was the main predictor of belief. The relationship between belief and cognition was more complex; it was dependent on what type of belief was active. Paranormal belief required a more intuitive thinking style to be present, whereas religious belief could withstand a reflective mind set. This thesis develops a new scale that measures supernatural belief provides a unique contribution to knowledge by establishing a model of cognition, personality and belief.the Bial Foundation, Porto (Grant Number: 355/14)