Objective Bayesian hypothesis testing in binomial regression models with integral prior distributions

Salmeron, Diego; Cano, Juan Antonio; Robert, Christian P.

Salmeron, Diego; Cano, Juan Antonio; Robert, Christian P. (2015), Objective Bayesian hypothesis testing in binomial regression models with integral prior distributions, Statistica Sinica, 25, 3, p. 1009-1024. 10.5705/ss.2013.338

Type

Article accepté pour publication ou publié

External document link

https://arxiv.org/abs/1306.6928v1

Date

2015

Journal name

Statistica Sinica

Volume

Number

Publisher

Institute of Statistical Science

Published in

Paris

Pages

1009-1024

Abstract (EN)

In this work we apply the methodology of integral priors to deal with Bayesian model selection in nested binomial regression models with a general link function. These models are often used to investigate associations and risks in epidemiological studies where one goal is to find whether or not an exposure is a risk factor for developing a certain disease; the purpose of the current paper is to test the effect of specific exposure factors. We formulate the problem as a Bayesian model selection one and solve it using objective Bayes factors. To elicit prior distributions on the regression coefficients of the binomial regression models, we rely on the methodology of integral priors that is nearly automatic as it only requires the specification of estimation reference priors and it does not depend on tuning parameters or on hyperparameters.

Subjects / Keywords

Markov chain; Integral prior; Jeffreys prior; Objective Bayes factor; Binomial regression mod

JEL

C11 - Bayesian Analysis: General