Browsing by Author "Iglesias, PL"

Now showing 1 - 3 of 3
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    A Gibbs sampling scheme to the product partition model: an application to change-point problems
    (PERGAMON-ELSEVIER SCIENCE LTD, 2003) Loschi, RH; Cruz, FRB; Iglesias, PL; Arellano Valle, RB
    This paper extends previous results for the classical product partition model applied to the identification of multiple change points in the means and variances of time series. Prior distributions for these two parameters and for the probability p that a change takes place at a particular period of time are considered and a new scheme based on Gibbs sampling to estimate the posterior relevances of the model is proposed. The resulting algorithm is applied to the analysis of two Brazilian stock market data. The computational experiments seem to indicate that the algorithm runs fast in common PC-like machines and it may be a useful tool for analyzing change-point problems.
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    Bayesian clustering and product partition models
    (BLACKWELL PUBL LTD, 2003) Quintana, FA; Iglesias, PL
    We present a decision theoretic formulation of product partition models (PPMs) that allows a formal treatment of different decision problems such as estimation or hypothesis testing and clustering methods simultaneously. A key observation in our construction is the fact that PPMs can be formulated in the context of model selection. The underlying partition structure in these models is closely related to that arising in connection with Dirichlet processes. This allows a straightforward adaptation of some computational strategies-originally devised for nonparametric Bayesian problems-to our framework. The resulting algorithms are more flexible than other competing alternatives that are used for problems involving PPMs. We propose an algorithm that yields Bayes estimates of the quantities of interest and the groups of experimental units. We explore the application of our methods to the detection of outliers in normal and Student t regression models, with clustering structure equivalent to that induced by, a Dirichlet process prior. We also discuss the sensitivity of the results considering different prior distributions for the partitions.
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    Predictivistic characterizations of multivariate student-t models
    (ACADEMIC PRESS INC ELSEVIER SCIENCE, 2003) Loschi, RH; Iglesias, PL; Arellano Valle, RB
    De Finetti style theorems characterize models (predictive distributions) as mixtures of the likelihood function and the prior distribution, beginning from some judgment of invariance about observable quantities. The likelihood function generally has its functional form identified from invariance assumptions only. However, we need additional conditions on observable quantities (typically, assumptions on conditional expectations) to identify the prior distribution. In this paper, we consider some well-known invariance assumptions and establish additional conditions on observable quantities in order to obtain a predictivistic characterization of the multivariate and matrix-variate Student-t distributions as well as for the Student-t linear model. As a byproduct, a characterization for the Pearson type 11 distribution is provided. (C) 2003 Elsevier Science (USA). All rights reserved.