Assessing Multinomial Distributions with a Bayesian Approach

Abstract

This paper introduces a unified Bayesian approach for testing various hypotheses related to multinomial distributions. The method calculates the Kullback–Leibler divergence between two specified multinomial distributions, followed by comparing the change in distance from the prior to the posterior through the relative belief ratio. A prior elicitation algorithm is used to specify the prior distributions. To demonstrate the effectiveness and practical application of this approach, it has been applied to several examples.

Keywords

• dirichlet distribution
• hypothesis testing
• Kullback–Leibler divergence
• multinomial distribution
• relative belief inferences