Autore
Liseo, Brunero

Titolo
Robustness issues in Bayesian model selection
Periodico
Università degli Studi di Roma "La Sapienza" - Dipartimento di Studi Geoeconomici, Linguistici, Statistici e Storici per l'Analisi regionale. Working papers
Anno: 1999 - Fascicolo: 12 - Pagina iniziale: 1 - Pagina finale: 24

One of the most prominent goals of Bayesian robustness is to study the sensitivity of final answers to the various inputs of a statistical analysis. Also, since the use of extra-experimental information (typically in the form of a prior distribution over the unknown "elements" of a model) is perceived as the most discriminating feature of the Bayesian approach to inference, sensitivity to the prior has become perhaps the most relevant topic of Bayesian robustness. On the other hand, the influence of the prior on the final answer of a statistical inference not always has the same importance. In estimation problems, for example, priors are often picked for convenience, for, if the sample size is fairly large, the effect of the prior gets smaller. But, this is not the case in model selection and hypothesis testing. Both Bayes factors and other alternative Bayesian tools are quite sensitive to the choice of the prior distribution and this phenomenon does not vanish as the sample size gets larger. This makes the role of Bayesian robustness crucial in the theory and practice of Bayesian model selection, and indicate the ways how robust Bayesian techniques can be a valuable tool in the model choice process. Due to the prominet role of Bayes factors in model selection problems, we will discuss in detail sensitivity of Bayes factors (and their recent ramifications) to prior distribution. Examples of theoretical interest (Precise hypothesis testing, default analysis of mixture models) will also be presented




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