This paper concerns the calculation of Bayes estimators of ratios of outcome proportions generated by the replication of an arbitrary tree-structured compound Bernoulli experiment under a multinomial-type sampling scheme. Here the compound Bernoulli experiment is treated as a collection of linear sequences of independent generalized Bernoulli trials having Dirichlet type 1 prior probability distributions. A method of obtaining a closed-form expression of the cumulative distribution function of the ratio of proportions -from its Meijer G-function representation -is described. Bayes point and interval estimators are directly obtained from the properties the distribution function as well as its related probability density function. In addition, the density function is used to derive the probability mass function of the predictive distribution any two associated outcome categories of the experiment -under an inverse multinomial-type sampling scheme. An illustrative numerical example concerning a Bayesian analysis of a simple tree-structured mortality model for medical patients who have su ered an acute myocardial infarction (heart attack) is also included.