Robust Bayesian model selection for heavy-tailed linear regression using\n finite mixtures

2015/09/01 by Flávio B. Gonçalves, Gonçalves, Flávio B, Marcos O. Prates +3
Computer Science · Mathematics · #Bayesian Methods and Mixture Models #Statistical Methods and Bayesian Inference #Statistical Methods and Inference

paper · pdf · doi:10.48550/arxiv.1509.00331

Abstract

In this paper we present a novel methodology to perform Bayesian model\nselection in linear models with heavy-tailed distributions. We consider a\nfinite mixture of distributions to model a latent variable where each component\nof the mixture corresponds to one possible model within the symmetrical class\nof normal independent distributions. Naturally, the Gaussian model is one of\nthe possibilities. This allows for a simultaneous analysis based on the\nposterior probability of each model. Inference is performed via Markov chain\nMonte Carlo - a Gibbs sampler with Metropolis-Hastings steps for a class of\nparameters. Simulated examples highlight the advantages of this approach\ncompared to a segregated analysis based on arbitrarily chosen model selection\ncriteria. Examples with real data are presented and an extension to censored\nlinear regression is introduced and discussed.\n

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