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An up-to-date, comprehensive account of major issues in finite mixture modeling This volume provides an up-to-date account of the theory and applications of modeling via finite mixture distributions. With an emphasis on the applications of mixture models in both mainstream analysis and other areas such as unsupervised pattern recognition, speech recognition, and medical imaging, the book describes the formulations of the finite mixture approach, details its methodology, discusses aspects of its implementation, and illustrates its application in many common statistical contexts

Finite mixture distributions are a weighted average of a ¯nite number of distributions. The latter are usually called the mixture components. The weights are usually described by a multinomial distribution and are sometimes called mixing proportions. The mixture components may be the same type of distributions with di®erent parameter values but they may also be completely di®erent distributions (Everitt and Hand, 1981; Titterington et al., 1985). Therefore, ¯nite mixture distributions are very °exible for modeling data. They are frequently used as a building block within many modern econometric models. The speci¯cation of the mixture distribution depends on the modeling problem at hand. In this thesis, we introduce new applications of ¯nite mixtures to deal with several di®erent modeling issues. Each chapter of the thesis focusses on a speci¯c modeling issue. The parameters of some of the resulting models can be estimated using standard techniques but for some of the chapters we need to develop new estimation and inference methods. To illustrate how the methods can be applied, we analyze at least one empirical data set for each approach. These data sets cover a wide range of research ¯elds, such as macroeconomics, marketing, and political science. We show the usefulness of the methods and, in some cases, the improvement over previous methods in the literature.

The standard mixture model, the concomitant variable mixture model, the mixture regression model and the concomitant variable mixture regression model all enable simultaneous identification and description of groups of observations. This study reviews the different ways in which dependencies among the variables involved in these models are accommodated. It is demonstrated that the standard and concomitant variable mixture models identify groups of observations and at the same time discriminate them analogous, respectively, to discriminant analysis and logistic regression. While the mixture regression model is shown to have limited use for classifying new observations. An extension of it, called the saturated mixture regression model, is shown to be more useful in that respect. Advantages of that model in model estimation when missing data are present and as a framework for model selection are also discussed.

Numerous kinds of uncertainties may affect an economy, e.g. economic, political, and en- vironmental ones. We model the aggregate impact by the uncertainties on an economy and its associated financial market by randomised mixtures of Lévy processes. We assume that mar- ket participants observe the randomised mixtures only through best estimates based on noisy market information. The concept of incomplete information introduces an element of stochastic filtering theory in constructing what we term "filtered Esscher martingales". We make use of this family of martingales to develop pricing kernel models. Examples of bond price models are examined, and we show that the choice of the random mixture has a significant effect on the model dynamics and the types of movements observed in the associated yield curves. Parameter sensitivity is analysed and option price processes are derived. We extend the class of pricing kernel models by considering a weighted heat kernel approach, and develop models driven by mixtures of Markov processes.

"This paper is concerned with estimating preference functionals for choice under risk from the choice behaviour of individuals. We note that there is heterogeneity in behaviour between individuals and within individuals. By 'heterogeneity between individuals' we mean that people are different, in terms of both their preference functionals and their parameters for these functionals. By 'heterogeneity within individuals' we mean that behaviour may be different even by the same individual for the same choice problem. We propose methods of taking into account all forms of heterogeneity, concentrating particularly on using a Mixture Model to capture the heterogeneity of preference functionals." [author's abstract]