Title of dissertation: GLOBAL OPTIMIZATION OF FINITE MIXTURE MODELS Jeffrey W. Heath Doctor of Philosophy, 2007 Dissertation directed by: Professor Michael Fu Robert H. Smith School of Business & Professor Wolfgang Jank Robert H. Smith School of Business The Expectation-Maximization (EM) algorithm is a popular and convenient tool for the estimation of Gaussian mixture models and its natural ext...

In the applications of finite mixture of regression (FMR) models, often many covariates are used, and their contributions to the response variable vary from one component to another of the mixture model. This creates a complex variable selection problem. Existing methods, such as the Akaike information criterion and the Bayes information criterion, are computationally expensive as the number of...

Classical finite mixture regression is useful for modeling the relationship between scalar predictors and scalar responses arising from subpopulations defined by the di ering associations between those predictors and responses. The classical finite mixture regression model is extended to incorporate functional predictors by taking a wavelet-based approach in which both the functional predictors...

Positive Data Clustering Using Finite Inverted Dirichlet Mixture Models Taoufik BDIRI In this thesis we present an unsupervised algorithm for learning finite mixture models from multivariate positive data. Indeed, this kind of data appears naturally in many applications, yet it has not been adequately addressed in the past. This mixture model is based on the inverted Dirichlet distribution, whi...

We adopt a Bayesian approach to the analysis of six data sets recording foetal control mortality in mouse litters. We illustrate how a variety of diierent models may be considered, using Markov chain Monte Carlo (MCMC) simulation techniques, and compare the results with the corresponding maximum likelihood analyses. We present an auxiliary variable method for determining the probability that an...

Abstract— Image segmentation for robots requires to be fast, in order to deal with ever more powerful processors. Moreover, it is assumed to be robust to environmental changes, such as light conditions. In this paper we propose the application of a couple of unsupervised learning algorithms for the estimation of the number of components and the parameters of a mixture model for image segmentati...

In finite mixture models, apart from underlying mixing measure, true kernel density function of each subpopulation in the data is, in many scenarios, unknown. Perhaps the most popular approach is to choose some kernel functions that we empirically believe our data are generated from and use these kernels to fit our models. Nevertheless, as long as the chosen kernel and the true kernel are diffe...

An extension of latent class (LC) and finite mixture models is described for the analysis of hierarchical data sets. As is typical in multilevel analysis, the dependence between lower-level units within higher-level units is dealt with by assuming that certain model parameters differ randomly across higher-level observations. One of the special cases is an LC model in which group-level differen...

Developing sound or reliable statistical models for analyzing motor vehicle crashes is very important in highway safety studies. However, a significant difficulty associated with the model development is related to the fact that crash data often exhibit over-dispersion. Sources of dispersion can be varied and are usually unknown to the transportation analysts. These sources could potentially af...

Parametric mixture models are commonly used in applied work, especially empirical economics, where these models are often employed to learn for example about the proportions of various types in a given population. This paper examines the inference question on the proportions (mixing probability) in a simple mixture model in the presence of nuisance parameters when sample size is large. It is we...