[pt] O objetivo primordial desta tese é descrever e discutir um método para previsão de séries temporais que apresentam descontinuidades bruscas - o chamado Método Bayesiano de Crescimento Linear de Estados Múltiplos (MCL-EM), desenvolvido por Harrison e Stevens. Na primeira parte é feito um rápido apanhado dos métodos existentes para previsão de séries temporais e seu relacionamento com métodos bayesianos mais gerais. A seguir é apresentado o MCL-EM e comparado com os principais métodos clássicos de crescimento linear. Finalmente são apresentadas algumas aplicações a séries reais e simuladas e analisadas suas vantagens e desvantagens em relação aos demais métodos em geral. / [en] The main objective of this dissertation is to describe and discuss a forecasting method for time series subject to sudden discontinuities - the so called multi-state linear Growth Bayesian Method (MLG for short), developped by Harrison and Stevens. The first part consists of a brief revision of the existing time series forecasting methods and their relationships with the more general bayesian methods. It is followed by a description of the MLG and its comparison with the classical linear growth methods. Finally, some applications to real and simulated time series are presented and its advantages and drawbaks are thoroughly discussed.

BACKGROUND: Chronic ankle instability (CAI) patients have varying levels of mechanical and sensorimotor impairments that may lead to disparate functional movement patterns. Current literature on landing biomechanics in a CAI population, however, considers all patients as a homogeneous group. In our prior work, we identified 6 subgroups of movement patterns using lower extremity kinematics during a landing/cutting task and that showed promise in furthering understanding of movement patterns in a laboratory-based environment. To increase the utility of this methodology in clinical settings, there is a need to find easily administered clinical tests that can help identify multiple subgroups of movement patterns in a CAI population. The purpose of the present study was to identify clinical tests that would help identify frontal and sagittal kinematic movement pattern subgroups during a landing/cutting task. We hypothesized that clinical tests would help predict group assignment; which CAI patient is assigned to frontal and sagittal kinematic movement pattern subgroups, respectively. METHODS: We recruited 100 CAI patients from a university population. We used three-dimensional instrumented motion analysis to capture ankle, knee and hip kinematics as subjects performed a single-leg maximal jump landing/cutting task. We used sagittal and frontal joint angle waveforms to group CAI patients. We then used 12 demographic and clinical measures to predict these subgroups of CAI. These consisted of gender, Star Excursion Balance Test-Anterior (SEBT-ANT), Biodex static balance, figure 8 hop, triple crossover hop, dorsiflexion range of motion (DFROM), number of failed trials, body mass index, a score of Foot and Ankle Ability Measure-Activities of Daily Living (FAAM-ADL), a score of FAAM-Sports, number of "yes" responses on Modified Ankle Instability Index, and number of previous ankle sprains. First, we used functional principal component analysis to create representative curves for each CAI patient and plane from the 3 lower extremity joint angles. We then used these curves as inputs to a predictor-dependent product partition model to cluster each CAI patient to unique subgroups. Finally, we used a multinomial prediction model to examine the accuracy of predicting group membership from demographic and clinical metrics. RESULTS: The predictor-dependent product partition model identified 4 frontal and 5 sagittal movement pattern subgroups. Six predictors (e.g., gender, SEBT-ANT, figure 8 hop, triple crossover hop, DFROM, and FAAM-ADL) predicted group membership with 55.7% accuracy for frontal subgroups. Ten predictors (minus Biodex static balance and number of previous ankle sprains) predicted group membership with 59% accuracy for sagittal subgroups. CONCLUSION: Novel statistical analyses allowed us to predict group membership for multiple frontal and sagittal kinematic movement patterns during landing/cutting using a series of clinical predictors. However, due to relatively lower accuracy (56–59% accuracy), the clinical utility of the current prediction model may be limited. Future work should consider including other clinical predictors to maximize prediction accuracy for identifying multiple kinematic movement patterns during a landing/cutting task.

No description available.

<p>An important question in biology is the identification of functionally important sites and regions in proteins. A variety of statistical phylogenetic models have been developed to predict functionally important protein sites, e.g. ligand binding sites or protein-protein interaction interfaces, by comparing sequences from different species. However, most of the existing methods ignore the spatial clustering of functionally important sites in protein tertiary/primary structures, which significantly reduces their power to identify functionally important regions in proteins. In this thesis, we present several new statistical phylogenetic models for inferring functionally important protein regions in which Gaussian processes or hidden Markov models are used as prior distributions to model the spatial correlation of evolutionary patterns in protein tertiary/ primary structures. Both simulation studies and empirical data analyses suggest that these new models outperform classic phylogenetic models. Therefore, these new models may be useful tools for extracting functional insights from protein sequences and for guiding mutagenesis experiments. Furthermore, the new methodologies developed in these models may also be used in the development of new statistical models to answer other important questions in phylogenetics and molecular evolution.</p> / Doctor of Philosophy (PhD)

Bayesian Model Averaging (BMA) is a new area in modern applied statistics that provides data analysts with an efficient tool for discovering promising models and obtaining esti-mates of their posterior probabilities via Markov chain Monte Carlo (MCMC). These probabilities can be further used as weights for model averaged predictions and estimates of the parameters of interest. As a result, variance components due to model selection are estimated and accounted for, contrary to the practice of conventional data analysis (such as, for example, stepwise model selection). In addition, variable activation probabilities can be obtained for each variable of interest. This dissertation is aimed at connecting BMA and various ramifications of the multivari-ate technique called Reduced-Rank Regression (RRR). In particular, we are concerned with Canonical Correspondence Analysis (CCA) in ecological applications where the data are represented by a site by species abundance matrix with site-specific covariates. Our goal is to incorporate the multivariate techniques, such as Redundancy Analysis and Ca-nonical Correspondence Analysis into the general machinery of BMA, taking into account such complicating phenomena as outliers and clustering of observations within a single data-analysis strategy. Traditional implementations of model averaging are concerned with selection of variables. We extend the methodology of BMA to selection of subgroups of observations and im-plement several approaches to cluster and outlier analysis in the context of the multivari-ate regression model. The proposed algorithm of cluster analysis can accommodate re-strictions on the resulting partition of observations when some of them form sub-clusters that have to be preserved when larger clusters are formed. / Ph. D.

Ecological data is often fraught with many problems such as Missing Data and Spatial Correlation. In this dissertation we use a data set collected by the Ohio EPA as motivation for studying techniques to address these problems. The data set is concerned with the benthic health of Ohio's waterways. A new method for incorporating covariate structure and missing data mechanisms into missing data analysis is considered. This method allows us to detect relationships other popular methods do not allow. We then further extend this method into model selection. In the special case where the unobserved covariates are assumed normally distributed we use the Bayesian Model Averaging method to average the models, select the highest probability model and do variable assessment. Accuracy in calculating the posterior model probabilities using the Laplace approximation and an approximation based on the Bayesian Information Criterion (BIC) are explored. It is shown that the Laplace approximation is superior to the BIC based approximation using simulation. Finally, Hierarchical Spatial Linear Models are considered for the data and we show how to combine analysis which have spatial correlation within and between clusters. / Ph. D.

L’objectif de cette thèse est la mise en place d’un Système d’Alerte Précoce comme instrument de prévision de la survenance des crises bancaires et des crises de la dette souveraine dans 48 pays de 1977 à 2010. Il s’agit à la fois d’identifier les facteurs capables de prédire ces événements et ceux annonçant leurs interactions éventuelles. La présente étude propose une approche à la fois originale et robuste qui tient compte de l’incertitude des modèles et des paramètres par la méthode de combinaison bayésienne des modèles de régression ou Bayesian Model Averaging (BMA). Nos résultats montrent que les avoirs étrangers nets en pourcentage du total des actifs, la dette à court terme en pourcentage des réserves totales et enfin la dette publique en pourcentage du PIB ont un pouvoir prédictif élevé pour expliquer les crises de la dette souveraine pour plusieurs pays. De plus, la croissance de l’activité et du crédit bancaire, le degré de libéralisation financière et le poids de la dette extérieure sont des signaux décisifs des crises bancaires. Notre approche offre le meilleur compromis entre les épisodes manqués et les fausses alertes. Enfin, nous étudions le lien entre les crises bancaires et les crises de la dette souveraine pour 62 pays de 1970 à 2011, en développant une approche basée sur un modèle Vecteur Auto-Régressif (VAR). Nos estimations montrent une relation significative et bidirectionnelle entre les deux types d’évènements. / The main purpose of this thesis is the development of an Early Warning System to predict banking and sovereign debt crises in 48 countries from 1977 to 2010. We are interested in identifying both factors that predict these events and those announcing their possible interactions. In particular, our empirical works provide an original and robust approach accounting for model and parameter uncertainty by means of the Bayesian Model Averaging method. Our results show that: Net foreign assets to total assets, short term debt to total reserves, and public debt to GDP have a high predictive power to signal sovereign debt crises in many countries. Furthermore, the growth rates of economic activity and credit, financial liberalization, and the external indebtedness are decisive signals of banking crises. Our approach offers the best compromise between missed episodes and false alarms. Finally, we study the link between banking and sovereign debt crises for 62 countries from 1970 to 2011 by developing an approach based on a Vector Autoregressive model (VAR). Our estimates show a significant two-way relationship between the two types of events.

This study suggests a two-step approach to identifying and interpreting regional convergence clubs in Europe. The first step involves identifying the number and composition of clubs using a space-time panel data model for annual income growth rates in conjunction with Bayesian model comparison methods. A second step uses a Bayesian space-time panel data model to assess how changes in the initial endowments of variables (that explain growth) impact regional income levels over time. These dynamic trajectories of changes in regional income levels over time allow us to draw inferences regarding the timing and magnitude of regional income responses to changes in the initial conditions for the clubs that have been identified in the first step. This is in contrast to conventional practice that involves setting the number of clubs ex ante, selecting the composition of the potential convergence clubs according to some a priori criterion (such as initial per capita income thresholds for example), and using cross-sectional growth regressions for estimation and interpretation purposes. (authors' abstract)

Sequential experimentation is often employed in process optimization wherein a series of small experiments are run successively in order to determine which experimental factor levels are likely to yield a desirable response. Although there currently exists a framework for identifying optimal follow-up designs after an initial experiment has been run, the accepted methods frequently point to multiple designs leaving the practitioner to choose one arbitrarily. In this thesis, we apply preposterior analysis and Bayesian model-averaging to develop a methodology for further discriminating between optimal follow-up designs while controlling for both parameter and model uncertainty.

This paper presents a comprehensive review and comparison of five computational methods for Bayesian model selection, based on MCMC simulations from posterior model parameter distributions. We apply these methods to a well-known and important class of models in financial time series analysis, namely GARCH and GARCH-t models for conditional return distributions (assuming normal and t-distributions). We compare their performance vis--vis the more common maximum likelihood-based model selection on both simulated and real market data. All five MCMC methods proved feasible in both cases, although differing in their computational demands. Results on simulated data show that for large degrees of freedom (where the t-distribution becomes more similar to a normal one), Bayesian model selection results in better decisions in favour of the true model than maximum likelihood. Results on market data show the feasibility of all model selection methods, mainly because the distributions appear to be decisively non-Gaussian. / Series: Report Series SFB "Adaptive Information Systems and Modelling in Economics and Management Science"