Bayesian Inference for a Hidden Truncated Bivariate Exponential Distribution with Applications

Abstract

In many real-life scenarios, one variable is observed only if the other concomitant variable or the set of concomitant variables (in the multivariate scenario) is truncated from below, above, or from a two-sided approach. Hidden truncation models have been applied to analyze data when bivariate or multivariate observations are subject to some form of truncation. While the statistical inference for hidden truncation models (truncation from above) under the frequentist and the Bayesian paradigms has been adequately discussed in the literature, the estimation of a two-sided hidden truncation model under the Bayesian framework has not yet been discussed. In this paper, we consider the Bayesian inference for a general two-sided hidden truncation model based on the Arnold–Strauss bivariate exponential distribution. In addition, a Bayesian model selection approach based on the Bayes factor to select between models without truncation, with truncation from below, from above, and two-sided truncation is also explored. An extensive simulation study is carried out for varying parameter choices under the conjugate prior set-up. For illustrative purposes, a real-life dataset is re-analyzed to demonstrate the applicability of the proposed methodology.

Keywords

• Bayes factor
• bivariate exponential distribution
• Gibbs sampling
• hidden truncation
• informative prior
• posterior probability