Table of Contents
Advances in Statistics
Volume 2014, Article ID 504325, 8 pages
http://dx.doi.org/10.1155/2014/504325
Research Article

A Focused Bayesian Information Criterion

1Biostatistics Unit, Department of Public Health, University of Yaoundé I, P.O. Box 1364, Yaoundé, Cameroon
2Theoretical Biology and Biophysics, Group T-6, Los Alamos National Laboratory, Los Alamos, NM 87545, USA

Received 31 May 2014; Revised 18 September 2014; Accepted 25 September 2014; Published 14 October 2014

Academic Editor: Vito Mr Muggeo

Copyright © 2014 Georges Nguefack-Tsague and Ingo Bulla. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

Myriads of model selection criteria (Bayesian and frequentist) have been proposed in the literature aiming at selecting a single model regardless of its intended use. An honorable exception in the frequentist perspective is the “focused information criterion” (FIC) aiming at selecting a model based on the parameter of interest (focus). This paper takes the same view in the Bayesian context; that is, a model may be good for one estimand but bad for another. The proposed method exploits the Bayesian model averaging (BMA) machinery to obtain a new criterion, the focused Bayesian model averaging (FoBMA), for which the best model is the one whose estimate is closest to the BMA estimate. In particular, for two models, this criterion reduces to the classical Bayesian model selection scheme of choosing the model with the highest posterior probability. The new method is applied in linear regression, logistic regression, and survival analysis. This criterion is specially important in epidemiological studies in which the objective is often to determine a risk factor (focus) for a disease, adjusting for potential confounding factors.