One of the most important goals of unsupervised learning is to discover meaningful clusters in data. Clustering algorithms strive to discover groups, or clusters, of data points which belong together because they are in some way similar. The research presented in this thesis focuses on using Bayesian statistical techniques to cluster data. We take a model-based Bayesian approach to defining a c...

This paper gives an introduction to the use of variational methods in Bayesian inference and shows how variational methods can be used to approximate the intractable posterior distributions which arise in this kind of inference. The flexibility of these approximations allows us to include positivity constraints when attempting to infer hidden pixel intensities in images. The approximating poste...

Empirical data are almost always lacking in real-world risk analyses. In fact, some risk analysis problems try to forecast what risks may be associated with situations that are, at the time of the assessment, only hypothetical. It may therefore be impractical, unethical, or even impossible to collect relevant empirical data. To make matters worse for the analyst, the situations of concern in ri...

Bayesian inference has become increasingly important in statistical machine learning. Exact Bayesian calculations are often not feasible in practice, however. A number of approximate Bayesian methods have been proposed to make such calculations practical, among them the variational Bayesian (VB) approach. The VB approach, while useful, can nevertheless suffer from slow convergence to the approx...

Bayesian statistical methods provide a flexible and principled framework for relating cognitive models to behavioral data. They allow for cognitive models to be formalized, evaluated, and applied, supporting inferences about parameters, the testing of models, and making predictions about data. This chapter argues that Bayesian methods are most useful for cognitive modeling in allowing more ambi...

Ecosystems are dynamic in both space and time, hence involve multiple spatial and temporal scales, and are often heterogeneous in both of those dimensions, leading to spatial and temporal clustering. Accommodating this complexity in the context of scientific (statistical) hypothesis testing necessitates more advanced methods than those available within the classical null hypothesis testing para...