Bakgrund: Tidigare studier har identifierat flera riskfaktorer, såsom kost, fysisk aktivitet och BMI, gällande kolorektal cancer. Att analysera kost utifrån kostmönster istället för enskilda livsmedel har visat sig vara effektivt för att undersöka risker för kolorektal cancer. Datamaterial samlades in med hjälp av en fall-kontroll studie med 257 fall och 805 kontroller. Syfte: Identifiera faktorer som ger en höjd eller sänkt risk för kolorektal cancer utifrån områdena kost, fysisk aktivitet och BMI. Metod: Faktoranalys användes för att upptäcka kostmönster. Logistisk regression användes för att skatta oddskvoter och 95 % konfidensintervall. Resultat: Tio stycken kostmönster erhölls från faktoranalysen. Kostmönstren ”Läsk, juice och mjölkprodukter” (OR=1,288; ORQ4=2,159), ”Te, men inte kaffe”(OR=1,228; ORQ3=1,891; ORQ4=1,668) och ”Fågel, rött kött och fisk”( ORQ4=1,724) gav alla en ökad risk. Däremot visade kostmönstret ”Mat från säd och ost”( ORQ2=0,546; ORQ4=0,592) en minskad risk. BMI för tio år sedan (OR=1,079; ORÖvervikt=1,491; ORFetma=2,260) identifierades som en riskfaktor. Att arbeta inom stillasittande (OR=0,975; OR>15 år=0,517) och mellanaktiva (OR=0,977; OR6-10 år=0,497;OR>15 år=0,565) yrken visade på en minskad risk. Slutsats: Flera kostmönster visade sig vara riskfaktorer, detta gäller även BMI för tio år sedan. Kostmönstret ”Mat från säd och ost” och att arbeta i fysiskt lätta till medeltunga yrken visade sig vara skyddande faktorer. / Background: Previous studies have shown several risk factors for developing colorectal cancer such as diet, physical activity and BMI. The method of analyzing diets based on dietary patterns, rather than individual food items, have been shown to be effective when investigating the colorectal cancer risk. The data was collected using a case-control study of 257 cases and 805 controls. Aim: Identify factors that cause increased or decreased risk in developing colorectal cancer based on diet, physical activity and BMI. Methods: Factor analysis was conducted to identify dietary patterns. Logistic regression was used to estimate odds ratio and 95 % confidence interval. Results: Factor analysis conducted ten dietary patterns, three of these patterns showed an increased risk “Soft drinks, juice and milk products” (OR=1,288; ORQ4=2,159), “Tea, but not coffee” (OR=1,228; ORQ3=1,891; ORQ4=1,668) and “Poultry, red meats and fish” (ORQ4=1,724).The dietary pattern “Food based on grain and cheese” (ORQ2=0,546; ORQ4=0,592) showed a decreased risk. BMI ten years ago (OR=1,079; OROverweight=1,491; ORObese=2,260) identified as a risk factor. To work in sedentary (OR=0,975; OR>15 years=0,517) or physically medium heavy (OR=0,977; OR6-10 years=0,497; OR>15 years=0,565) occupations indicated a decreased risk. Conclusions: Several dietary patterns has been identified as risk factors, this also includes BMI ten years ago. The dietary pattern “Food based on grain and cheese” and to work in sedentary or physically medium heavy occupations proved to be protective factors.

Les séquences protéiques naturelles sont le résultat net de l’interaction entre les mécanismes de mutation, de sélection naturelle et de dérive stochastique au cours des temps évolutifs. Les modèles probabilistes d’évolution moléculaire qui tiennent compte de ces différents facteurs ont été substantiellement améliorés au cours des dernières années. En particulier, ont été proposés des modèles incorporant explicitement la structure des protéines et les interdépendances entre sites, ainsi que les outils statistiques pour évaluer la performance de ces modèles. Toutefois, en dépit des avancées significatives dans cette direction, seules des représentations très simplifiées de la structure protéique ont été utilisées jusqu’à présent. Dans ce contexte, le sujet général de cette thèse est la modélisation de la structure tridimensionnelle des protéines, en tenant compte des limitations pratiques imposées par l’utilisation de méthodes phylogénétiques très gourmandes en temps de calcul. Dans un premier temps, une méthode statistique générale est présentée, visant à optimiser les paramètres d’un potentiel statistique (qui est une pseudo-énergie mesurant la compatibilité séquence-structure). La forme fonctionnelle du potentiel est par la suite raffinée, en augmentant le niveau de détails dans la description structurale sans alourdir les coûts computationnels. Plusieurs éléments structuraux sont explorés : interactions entre pairs de résidus, accessibilité au solvant, conformation de la chaîne principale et flexibilité. Les potentiels sont ensuite inclus dans un modèle d’évolution et leur performance est évaluée en termes d’ajustement statistique à des données réelles, et contrastée avec des modèles d’évolution standards. Finalement, le nouveau modèle structurellement contraint ainsi obtenu est utilisé pour mieux comprendre les relations entre niveau d’expression des gènes et sélection et conservation de leur séquence protéique. / Protein sequences are the net result of the interplay of mutation, natural selection and stochastic variation. Probabilistic models of molecular evolution accounting for these processes have been substantially improved over the last years. In particular, models that explicitly incorporate protein structure and site interdependencies have recently been developed, as well as statistical tools for assessing their performance. Despite major advances in this direction, only simple representations of protein structure have been used so far. In this context, the main theme of this dissertation has been the modeling of three-dimensional protein structure for evolutionary studies, taking into account the limitations imposed by computationally demanding phylogenetic methods. First, a general statistical framework for optimizing the parameters of a statistical potential (an energy-like scoring system for sequence-structure compatibility) is presented. The functional form of the potential is then refined, increasing the detail of structural description without inflating computational costs. Always at the residue-level, several structural elements are investigated: pairwise distance interactions, solvent accessibility, backbone conformation and flexibility of the residues. The potentials are then included into an evolutionary model and their performance is assessed in terms of model fit, compared to standard evolutionary models. Finally, this new structurally constrained phylogenetic model is used to better understand the selective forces behind the differences in conservation found in genes of very different expression levels.

Neural networks are powerful tools for modelling complex non-linear mappings, but they often suffer from overfitting and provide no measures of uncertainty in their predictions. Bayesian techniques are proposed as a remedy to these problems, as these both regularize and provide an inherent measure of uncertainty from their posterior predictive distributions. By quantifying predictive uncertainty, we attempt to improve a systematic trading strategy by scaling positions with uncertainty. Exact Bayesian inference is often impossible, and approximate techniques must be used. For this task, this thesis compares dropout, variational inference and Markov chain Monte Carlo. We find that dropout and variational inference provide powerful regularization techniques, but their predictive uncertainties cannot improve a systematic trading strategy. Markov chain Monte Carlo provides powerful regularization as well as promising estimates of predictive uncertainty that are able to improve a systematic trading strategy. However, Markov chain Monte Carlo suffers from an extreme computational cost in the high-dimensional setting of neural networks. / Neurala nätverk är kraftfulla verktyg för att modellera komplexa icke-linjära avbildningar, men de lider ofta av överanpassning och tillhandahåller inga mått på osäkerhet i deras prediktioner. Bayesianska tekniker har föreslagits för att råda bot på dessa problem, eftersom att de både har en regulariserande effekt, samt har ett inneboende mått på osäkerhet genom den prediktiva posteriora fördelningen. Genom att kvantifiera prediktiv osäkerhet försöker vi förbättra en systematisk tradingstrategi genom att skala modellens positioner med den skattade osäkerheten. Exakt Bayesiansk inferens är oftast omöjligt, och approximativa metoder måste användas. För detta ändamål jämför detta examensarbete dropout, variational inference och Markov chain Monte Carlo. Resultaten indikerar att både dropout och variational inference är kraftfulla regulariseringstekniker, men att deras prediktiva osäkerheter inte kan användas för att förbättra en systematisk tradingstrategi. Markov chain Monte Carlo ger en kraftfull regulariserande effekt, samt lovande skattningar av osäkerhet som kan användas för att förbättra en systematisk tradingstrategi. Dock lider Markov chain Monte Carlo av en enorm beräkningsmässig komplexitet i ett så högdimensionellt problem som neurala nätverk.

Control and monitoring networks often operate on AC/DC power systems. DC batteries and chargers are commonly used on industrial plants as auxiliary DC power systems for these control and monitoring networks. The energy demand and load profiles for these control networks differ from application to application. Proper design, sizing, and maintenance of the components that forms part of the DC control power system are therefore required. Throughout the load profile of a control and monitoring system there are various peak currents. The peak currents are classified as inrush and momentary loads. These inrush and momentary loads play a large role when calculating the required battery size for an application. This study investigates the feasibility of using supercapacitors in conjunction with batteries, in order to reduce the size of the required battery capacity. A reduction in the size of the required battery capacity not only influences the cost of the battery itself, but also influences the hydrogen emissions, the physical space requirements, and the required rectifiers and chargers. When calculating the required size batteries for an auxiliary power system, a defined load profile is required. Control and monitoring systems are used to control dynamic processes, which entails a continuous starting and stopping of equipment as the process demands. This starting and stopping of devices will cause fluctuations in the load profile. Ideally, data should be obtained from a live plant for the purpose of defining load profiles. Unfortunately, due to the economic risks involved, installing data logging equipment on a live industrial plant for the purpose of research, is not allowed. There are also no historical data available from which load profiles could be generated. In order to evaluate the influence of supercapacitors, complex load profiles are required. In this study, an alternative method of defining the load profile for a dynamic process is investigated. Load profiles for various applications are approximated using a probabilistic approach. The approximation methodology make use of plant operating philosophies as input to the Markov Chain Monte Carlo simulation theory. The required battery sizes for the approximated profiles are calculated using the IEEE recommended practice for sizing batteries. The approximated load profile, as well the calculated battery size are used for simulating the auxiliary power system. A supercapacitor is introduced into the circuit and the simulations are repeated. The introduction of the supercapacitor relieves the battery of the inrush and momentary loads of the load profile. The battery sizing calculations are repeated so as to test the influence of the supercapacitor on the required battery capacity. In order to investigate the full influence of adding a supercapacitor to the design, the impact on various factors are considered. In this study, these factors include the battery size, charger size, H2 extraction system, as well as maintenance requirements and the life of the battery. No major cost savings where evident from the results obtained. Primary reasons for this low cost saving are the fixed ranges in which battery sizes are available, as well as conservative battery data obtained from battery suppliers. It is believed that applications other than control and monitoring systems will show larger savings. / MIng (Computer and Electronic Engineering), North-West University, Potchefstroom Campus, 2015

Control and monitoring networks often operate on AC/DC power systems. DC batteries and chargers are commonly used on industrial plants as auxiliary DC power systems for these control and monitoring networks. The energy demand and load profiles for these control networks differ from application to application. Proper design, sizing, and maintenance of the components that forms part of the DC control power system are therefore required. Throughout the load profile of a control and monitoring system there are various peak currents. The peak currents are classified as inrush and momentary loads. These inrush and momentary loads play a large role when calculating the required battery size for an application. This study investigates the feasibility of using supercapacitors in conjunction with batteries, in order to reduce the size of the required battery capacity. A reduction in the size of the required battery capacity not only influences the cost of the battery itself, but also influences the hydrogen emissions, the physical space requirements, and the required rectifiers and chargers. When calculating the required size batteries for an auxiliary power system, a defined load profile is required. Control and monitoring systems are used to control dynamic processes, which entails a continuous starting and stopping of equipment as the process demands. This starting and stopping of devices will cause fluctuations in the load profile. Ideally, data should be obtained from a live plant for the purpose of defining load profiles. Unfortunately, due to the economic risks involved, installing data logging equipment on a live industrial plant for the purpose of research, is not allowed. There are also no historical data available from which load profiles could be generated. In order to evaluate the influence of supercapacitors, complex load profiles are required. In this study, an alternative method of defining the load profile for a dynamic process is investigated. Load profiles for various applications are approximated using a probabilistic approach. The approximation methodology make use of plant operating philosophies as input to the Markov Chain Monte Carlo simulation theory. The required battery sizes for the approximated profiles are calculated using the IEEE recommended practice for sizing batteries. The approximated load profile, as well the calculated battery size are used for simulating the auxiliary power system. A supercapacitor is introduced into the circuit and the simulations are repeated. The introduction of the supercapacitor relieves the battery of the inrush and momentary loads of the load profile. The battery sizing calculations are repeated so as to test the influence of the supercapacitor on the required battery capacity. In order to investigate the full influence of adding a supercapacitor to the design, the impact on various factors are considered. In this study, these factors include the battery size, charger size, H2 extraction system, as well as maintenance requirements and the life of the battery. No major cost savings where evident from the results obtained. Primary reasons for this low cost saving are the fixed ranges in which battery sizes are available, as well as conservative battery data obtained from battery suppliers. It is believed that applications other than control and monitoring systems will show larger savings. / MIng (Computer and Electronic Engineering), North-West University, Potchefstroom Campus, 2015

<p>Collections of large volumes of rich and complex data has become ubiquitous in recent years, posing new challenges in methodological and theoretical statistics alike. Today, statisticians are tasked with developing flexible methods capable of adapting to the degree of complexity and noise in increasingly rich data gathered across a variety of disciplines and settings. This has spurred the need for novel multivariate regression techniques that can efficiently capture a wide range of naturally occurring predictor-response relations, identify important predictors and their interactions and do so even when the number of predictors is large but the sample size remains limited. </p><p>Meanwhile, efficient model fitting tools must evolve quickly to keep pace with the rapidly growing dimension and complexity of data they are applied to. Aided by the tremendous success of modern computing, Bayesian methods have gained tremendous popularity in recent years. These methods provide a natural probabilistic characterization of uncertainty in the parameters and in predictions. In addition, they provide a practical way of encoding model structure that can lead to large gains in statistical estimation and more interpretable results. However, this flexibility is often hindered in applications to modern data which are increasingly high dimensional, both in the number of observations $n$ and the number of predictors $p$. Here, computational complexity and the curse of dimensionality typically render posterior computation inefficient. In particular, Markov chain Monte Carlo (MCMC) methods which remain the workhorse for Bayesian computation (owing to their generality and asymptotic accuracy guarantee), typically suffer data processing and computational bottlenecks as a consequence of (i) the need to hold the entire dataset (or available sufficient statistics) in memory at once; and (ii) having to evaluate of the (often expensive to compute) data likelihood at each sampling iteration. </p><p>This thesis divides into two parts. The first part concerns itself with developing efficient MCMC methods for posterior computation in the high dimensional {\em large-n large-p} setting. In particular, we develop an efficient and widely applicable approximate inference algorithm that extends MCMC to the online data setting, and separately propose a novel stochastic search sampling scheme for variable selection in high dimensional predictor settings. The second part of this thesis develops novel methods for structured sparsity in the high-dimensional {\em large-p small-n} regression setting. Here, statistical methods should scale well with the predictor dimension and be able to efficiently identify low dimensional structure so as to facilitate optimal statistical estimation in the presence of limited data. Importantly, these methods must be flexible to accommodate potentially complex relationships between the response and its associated explanatory variables. The first work proposes a nonparametric additive Gaussian process model to learn predictor-response relations that may be highly nonlinear and include numerous lower order interaction effects, possibly in different parts of the predictor space. A second work proposes a novel class of Bayesian shrinkage priors for multivariate regression with a tensor valued predictor. Dimension reduction is achieved using a low-rank additive decomposition for the latter, enabling a highly flexible and rich structure within which excellent cell-estimation and region selection may be obtained through state-of-the-art shrinkage methods. In addition, the methods developed in these works come with strong theoretical guarantees.</p> / Dissertation

This paper uses Bayesian model comparison methods to simultaneously specify both the spatial weight structure and explanatory variables for a spatial growth regression involving 255 NUTS 2 regions across 25 European countries. In addition, a correct interpretation of the spatial regression parameter estimates that takes into account the simultaneous feed- back nature of the spatial autoregressive model is provided. Our findings indicate that incorporating model uncertainty in conjunction with appropriate parameter interpretation decreased the importance of explanatory variables traditionally thought to exert an important influence on regional income growth rates. (authors' abstract)

A phylogenetic tree is used to model gene evolution and species evolution using molecular sequence data. For artifactual and biological reasons, a gene tree may differ from a species tree, a phenomenon known as gene tree-species tree incongruence. Assuming the presence of one or more evolutionary events, e.g., gene duplication, gene loss, and lateral gene transfer (LGT), the incongruence may be explained using a reconciliation of a gene tree inside a species tree. Such information has biological utilities, e.g., inference of orthologous relationship between genes. In this thesis, we present probabilistic models and methods for orthology analysis and species tree inference, while accounting for evolutionary factors such as gene duplication, gene loss, and sequence evolution. Furthermore, we use a probabilistic LGT-aware model for inferring gene trees having temporal information for duplication and LGT events. In the first project, we present a Bayesian method, called DLRSOrthology, for estimating orthology probabilities using the DLRS model: a probabilistic model integrating gene evolution, a relaxed molecular clock for substitution rates, and sequence evolution. We devise a dynamic programming algorithm for efficiently summing orthology probabilities over all reconciliations of a gene tree inside a species tree. Furthermore, we present heuristics based on receiver operating characteristics (ROC) curve to estimate suitable thresholds for deciding orthology events. Our method, as demonstrated by synthetic and biological results, outperforms existing probabilistic approaches in accuracy and is robust to incomplete taxon sampling artifacts. In the second project, we present a probabilistic method, based on a mixture model, for species tree inference. The method employs a two-phase approach, where in the first phase, a structural expectation maximization algorithm, based on a mixture model, is used to reconstruct a maximum likelihood set of candidate species trees. In the second phase, in order to select the best species tree, each of the candidate species tree is evaluated using PrIME-DLRS: a method based on the DLRS model. The method is accurate, efficient, and scalable when compared to a recent probabilistic species tree inference method called PHYLDOG. We observe that, in most cases, the analysis constituted only by the first phase may also be used for selecting the target species tree, yielding a fast and accurate method for larger datasets. Finally, we devise a probabilistic method based on the DLTRS model: an extension of the DLRS model to include LGT events, for sampling reconciliations of a gene tree inside a species tree. The method enables us to estimate gene trees having temporal information for duplication and LGT events. To the best of our knowledge, this is the first probabilistic method that takes gene sequence data directly into account for sampling reconciliations that contains information about LGT events. Based on the synthetic data analysis, we believe that the method has the potential to identify LGT highways. / <p>QC 20150529</p>

<p>This thesis presents Bayesian solutions to inference problems for three types of social network data structures: a single observation of a social network, repeated observations on the same social network, and repeated observations on a social network developing through time.</p><p>A social network is conceived as being a structure consisting of actors and their social interaction with each other. A common conceptualisation of social networks is to let the actors be represented by nodes in a graph with edges between pairs of nodes that are relationally tied to each other according to some definition. Statistical analysis of social networks is to a large extent concerned with modelling of these relational ties, which lends itself to empirical evaluation.</p><p>The first paper deals with a family of statistical models for social networks called exponential random graphs that takes various structural features of the network into account. In general, the likelihood functions of exponential random graphs are only known up to a constant of proportionality. A procedure for performing Bayesian inference using Markov chain Monte Carlo (MCMC) methods is presented. The algorithm consists of two basic steps, one in which an ordinary Metropolis-Hastings up-dating step is used, and another in which an importance sampling scheme is used to calculate the acceptance probability of the Metropolis-Hastings step.</p><p>In paper number two a method for modelling reports given by actors (or other informants) on their social interaction with others is investigated in a Bayesian framework. The model contains two basic ingredients: the unknown network structure and functions that link this unknown network structure to the reports given by the actors. These functions take the form of probit link functions. An intrinsic problem is that the model is not identified, meaning that there are combinations of values on the unknown structure and the parameters in the probit link functions that are observationally equivalent. Instead of using restrictions for achieving identification, it is proposed that the different observationally equivalent combinations of parameters and unknown structure be investigated a posteriori. Estimation of parameters is carried out using Gibbs sampling with a switching devise that enables transitions between posterior modal regions. The main goal of the procedures is to provide tools for comparisons of different model specifications.</p><p>Papers 3 and 4, propose Bayesian methods for longitudinal social networks. The premise of the models investigated is that overall change in social networks occurs as a consequence of sequences of incremental changes. Models for the evolution of social networks using continuos-time Markov chains are meant to capture these dynamics. Paper 3 presents an MCMC algorithm for exploring the posteriors of parameters for such Markov chains. More specifically, the unobserved evolution of the network in-between observations is explicitly modelled thereby avoiding the need to deal with explicit formulas for the transition probabilities. This enables likelihood based parameter inference in a wider class of network evolution models than has been available before. Paper 4 builds on the proposed inference procedure of Paper 3 and demonstrates how to perform model selection for a class of network evolution models.</p>

In this thesis, we consider some popular stochastic differential equation models used in finance, such as the Vasicek Interest Rate model, the Heston model and a new fractional Heston model. We discuss how to perform inference about unknown quantities associated with these models in the Bayesian framework. We describe sequential importance sampling, the particle filter and the auxiliary particle filter. We apply these inference methods to the Vasicek Interest Rate model and the standard stochastic volatility model, both to sample from the posterior distribution of the underlying processes and to update the posterior distribution of the parameters sequentially, as data arrive over time. We discuss the sensitivity of our results to prior assumptions. We then consider the use of Markov chain Monte Carlo (MCMC) methodology to sample from the posterior distribution of the underlying volatility process and of the unknown model parameters in the Heston model. The particle filter and the auxiliary particle filter are also employed to perform sequential inference. Next we extend the Heston model to the fractional Heston model, by replacing the Brownian motions that drive the underlying stochastic differential equations by fractional Brownian motions, so allowing a richer dependence structure across time. Again, we use a variety of methods to perform inference. We apply our methodology to simulated and real financial data with success. We then discuss how to make forecasts using both the Heston and the fractional Heston model. We make comparisons between the models and show that using our new fractional Heston model can lead to improve forecasts for real financial data.