Bayesian Methods for Mixture Modeling

This Master’s thesis is mostly focused on Bayesian methods for the selection and testing of discrete mixture models. The main problem that is studied in the project is the analysis of data sets of several categorical variables (e.g. test items, symptoms, genes) collected on a set of subjects. We fit a discrete mixture model to the data which means that the dependencies among the different variables are captured by a latent categorical variable. We assume that the manifest variables are independent given the latent variable. We implemented a Matlab program an exploratory data tool that searches for latent classes of interest for given data sets. Another problem studied in the project is the possibility of having missing observed data. For solving this problem we introduce an additional step in Gibbs sampling in which the values for the missing data are sampled. The methods described in the thesis are applied for a psychiatric diagnostics data set and for a data set containing information from schizophrenia affected and healthy persons. Bayesianska metoder för identifiering av sammansatta fördelningar