Bayesian Inference of Scale Parameters in Exponential Family Using Conditionally Specified Priors

Abstract

This article considers a unified Bayesian approach for comparing scale parameters in an exponential family, assuming other parameters such as location or shape, are known. Particular cases include the normal, gamma, Weibull, exponential, Poisson, and binomial distributions. Convenient conjugate priors are found in joint distribution conditionally specified. Hyperparameter elicitation techniques are discussed. The results are illustrated in the comparison of scales of two normals and two Weibull densities.

Key Words:

• Bayesian analysis
• Conjugate priors
• Exponential family
• Gibbs sampling
• Normal distribution
• Weibull distribution