Following the Loss Distribution Approach (LDA), this article develops two procedures for the simulation of an annual loss distribution for the modeling of operational risk. First, we provide an overview of the typical compound-process LDA used widely in operational risk modeling, before...

Modelling and inference with higher-dimensional variables, including studies in multivariate time series analysis, raise challenges to our ability to ``scale-up'' statistical approaches that involve both modelling and computational issues. Modelling issues relate to the interest in parsimony of...

We describe a class of sparse latent factor models, called graphical factor models (GFMs), and relevant sparse learning algorithms for posterior mode estimation. Linear, Gaussian GFMs have sparse, orthogonal factor loadings matrices, that, in addition to sparsity of the implied covariance...

Dynamic models, also termed state space models, comprise an extremely rich model class for time series analysis. This dissertation focuses on building state space models for a variety of contexts and computationally efficient methods for Bayesian inference for simultaneous estimation of latent...

The modelling and analysis of complex stochastic systems with increasingly large data sets, state-spaces and parameters provides major stimulus to research in Bayesian nonparametric methods and Bayesian computation. This dissertation presents advances in both nonparametric modelling and...

An important goal of research involving gene expression data for outcome prediction is to establish the ability of genomic data to define clinically relevant risk factors. Recent studies have demonstrated that microarray data can successfully cluster patients into low and high risk categories....

This thesis is concerned with the theoretical and practical aspects of some problems in Bayesian time series analysis and recursive estimation. In particular, we examine procedures for accommodating outliers in dynamic linear models which involve the use of heavy-tailed error distributions as...