Past Event: Oden Institute Seminar

On the Choice of the Prior Distribution in Bayesian Statistics

Fabrizio Ruggeri, Consiglio Nazionale delle Ricerche Istituto di Matematica Applicata e Tecnologie Informatiche

Abstract

Bayesian statistics has become very popular in the past decades, especially after the widespread diffusion of MCMC methods. Sophisticated models and simulation techniques have been proposed to address problems in engineering, finance, genomics, biostatistics, etc. but the excitement for all those new opportunities has somehow driven away the attention from a basic aspect of the Bayesian approach: the choice of the prior distribution in practice. The talk will critically review the typical textbook prior distributions, before presenting the main ideas of the robust Bayesian approach (Rios Insua and Ruggeri, 2000), which was mainly developed because of the impractical possibility of eliciting a prior distribution corresponding to the effective knowledge of the expert. Bayesian robustness is interested in modelling the uncertainty in the prior specification, e.g. with a class of priors, and then quantifying the influence of such uncertainty on the quantity of interest, e.g. through its spanned range when the prior varies in the class. Uncertainty affects not only priors but model (likelihood) and loss function as well. Despite of the plethora of proposed methods, Bayesian robustness (as envisioned in the book edited by Rios Insua and Ruggeri) is not common practice of Bayesian analysis, probably because of its mostly mathematical nature which makes it quite impractical, especially in absence of user-friendly software. Nonetheless, there is a need to incorporate it in Bayesian analysis, as well as methods for practically eliciting priors from the experts. Stemming from the experience with engineers and, recently, with physicians, some ad hoc methods applied to get information from them and translate it into prior distributions will be presented. Furthermore, methods will be presented to combine partial and incompatible opinions from more experts, or to use opinions on the quantiles of the distribution of the observable quantities, rather than directly on the parameters. The former method has been proposed in a context of e-democracy to combine opinions “quasi-automatically”, whereas the other comes from situations, typically described by extreme values distributions (e.g. flooding), for which it is difficult to get opinions directly on the parameters. [The talk is mostly devoted to people relatively new to Bayesian statistics, although “veterans” would find topics, like Bayesian robustness, which are not extensively considered nowadays and, possibly, some arguments to discuss about.] Rios Insua, D. and Ruggeri, F. Eds. (2000). Robust Bayesian Analysis, Lecture Notes in Statistics, Springer, New York. Fabrizio Ruggeri is Research Director in Milano at CNR-IMATI, a mathematical institute of the Italian National Research Council. An ASA fellow, he is the 2012 ISBA (International Society for Bayesian Analysis) President and former President of ENBIS (European Network for Business and Industrial Statistics). He is Editor-in-Chief of Applied Stochastic Models in Business and Industry and Encyclopedia of Statistics in Quality and Reliability, besides chairing the Applied Bayesian Statistics summer school and the workshops on Bayesian Inference in Stochastic Processes. His major interests are in Bayesian and industrial statistics.