Untitled - UFRJ

Particle LearningCarlos M. CarvalhoThe University of Chicago Booth School of Business, EUAMatt A. TaddyThe University of Chicago Booth School of Business, EUAThis short course describes the particle learning (PL) framework for sequential Bayesian inference.We introduce the ideas in the traditional context of state space models where the concepts of filteringsufficient statistics and the advantages of pre-selection particles are presented in details. The second partof the course turns the attention to the implementation of PL in general mixture models. In addition,we describe how the approach will apply to other models of current interest in the literature; it is hopedthat this will inspire a greater number of researchers to adopt sequential Monte Carlo methods for fittingtheir sophisticated mixture based models. Finally, we show that this particle learning approach leadsto straightforward tools for marginal likelihood calculation and posterior cluster allocation. Specificversions of the algorithm are derived for standard density estimation applications based on both finitemixture models and Dirichlet process mixture models, as well as for the less common settings of latentfeature selection through an Indian Buffet process and dependent distribution tracking through a probitstick- breaking model. We close by applying PL to Dynamic regression trees where a sequential treemodel is created whose state changes in time with the accumulation of new data, and provide particlelearning algorithms that allow for the efficient on-line posterior filtering of tree-states.8