BAYESIAN TESTING FOR INDEPENDENCE IN MARSHALL AND OLKIN’S BIVARIATE EXPONENTIAL MODEL

Jang Sik Cho (Korea), Chang Wan Kang (Korea) and Seung Bae Choi (Korea)

Received June 1, 2007

Abstract

In this paper, we propose a Bayesian testing procedure for independence in Marshall and Olkin’s bivariate exponential model based on Bayes factor. We use a noninformative prior such as an improper prior for the parameters so that such prior is defined only up to arbitrary constant which affects the values of Bayes factors. So we compute the fractional Bayes factor (FBF) proposed by O’Hagan [6] to compensate for that arbitrariness. We compute FBF’s and calculate the posterior probabilities for the hypotheses, respectively. We illustrate our procedure through a numerical example.

Keywords and phrases: Bayesian testing, bivariate exponential model, fractional Bayes factor, improper prior, Marshall and Olkin’s model, posterior probability.