In this thesis we consider some finite mixture time series models in which each component is following a well-known process, e.g. AR, ARMA or ARMA-GARCH process, with either normal-type errors or Student-t type errors. We develop MCMC methods and use them in the Bayesian analysis of these mixture models. We introduce some new models such as mixture of Student-t ARMA components and mixture of Student-t ARMA-GARCH components with complete Bayesian treatments. Moreover, we use component precision (instead of variance) with an additional hierarchical level which makes our model more consistent with the MCMC moves. We have implemented the proposed methods in R and give examples with real and simulated data.

Emerging sequencing approaches have revolutionized the way we can collect DNA sequence data for applications in bioforensics and biosurveillance. In this research, we present an approach to construct a database of known biological agents and use this database to develop a statistical framework to analyze raw reads from next-generation sequence data for species identification and strain attribution. Our method capitalizes on a Bayesian statistical framework that accommodates information on sequence quality, mapping quality and provides posterior probabilities of matches to a known database of target genomes. Importantly, our approach also incorporates the possibility that multiple species can be present in the sample or that the target strain is not even contained within the reference database. Furthermore, our approach can accurately discriminate between very closely related strains of the same species with very little coverage of the genome and without the need for genome assembly - a time consuming and labor intensive step. We demonstrate our approach using genomic data from a variety of known bacterial agents of bioterrorism and agents impacting human health.

In the framework of Bayesian model-based clustering based on a finite mixture of Gaussian distributions, we present a joint approach to estimate the number of mixture components and identify cluster-relevant variables simultaneously as well as to obtain an identified model. Our approach consists in specifying sparse hierarchical priors on the mixture weights and component means. In a deliberately overfitting mixture model the sparse prior on the weights empties superfluous components during MCMC. A straightforward estimator for the true number of components is given by the most frequent number of non-empty components visited during MCMC sampling. Specifying a shrinkage prior, namely the normal gamma prior, on the component means leads to improved parameter estimates as well as identification of cluster-relevant variables. After estimating the mixture model using MCMC methods based on data augmentation and Gibbs sampling, an identified model is obtained by relabeling the MCMC output in the point process representation of the draws. This is performed using K-centroids cluster analysis based on the Mahalanobis distance. We evaluate our proposed strategy in a simulation setup with artificial data and by applying it to benchmark data sets. (authors' abstract)

Non-intrusive load monitoring (NILM) refers to a set of statistical methods for inferring information about a household from its electricity load curve, without adding any additional sensor. The aim of this master thesis is to adapt NILM techniques for the assessment of the efficiency of retrofitting work to provide a first version of a retrofitting assessment tool. Two models are developed: a model corresponding to a constrained optimization problem, and a hierarchical Bayesian mixture model. These models are tested on a set of houses that have electric heating (which are the main target of retrofitting work). These models offer a satisfactory accuracy retrofitting assessment for about half of the houses. / Non-intrusive load monitoring (NILM) består av en uppsättning statistiska metoder för att härleda information om ett hushåll från belastningskurvan i bostaden, utan att lägga till ytterligare sensorer. Syftet med detta examensarbete är att anpassa NILM-teknikerna till utvärdering av energieffektivitet i energibyggnader och för att föreslå en första version av ett verktyg för utvärdering av effektiviteten i renoveringsarbeten. Två modeller föreslås: en modell som motsvarar ett begränsat optimeringsproblem och en hierarkisk Bayesiansk blandningsmodell. Modellerna testas på en uppsättning med elvärme (som är huvudmålet för renoveringsarbeten). De utvecklade modellerna gör det möjligt att upprå en tillfredsställande noggrannhet vid utvärderingen av arbeten för ungefär hälften av husen.

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