Bayes estimators of ratios of proportions between tree-structured experiments

Abstract

This paper concerns an inquiry into a Bayesian approach to comparing proportions between independent tree-structured compound Bernoulli experiments having multinomial-like sampling schemes. Inferences concerning the comparisons are based upon the properties of the prior distribution function of the ratio of proportions associated with any two inter-experiment outcome categories. A procedure for constructing the equational form of the cumulative distribution function of the ratio of proportions - from its inverse Mellin transform representation - is described. An illustrative numerical example involving a comparison of response proportions between independent instances of a tree-structured decision algorithm for the medical treatment of hypertension (high blood pressure) is also included.

Keywords:

• beta probability distribution
• Couchy residue theorem
• compound generalized Bernoulli experiment
• Dirichlet type I distribution
• hyper Dirichlet type I distribution
• Jordan's lemma
• Mellin transform
• multinamial distribution