Adaptive bayesian analysis for binomial proportions

Abstract

The authors consider the problem of statistical inference of binomial proportions for non-matched, correlated samples, under the Bayesian framework. Such inference can arise when the same group is observed at a different number of times with the aim of testing the proportion of some trait. For example, say, we are interested to infer about the effectiveness of a certain intervention teaching strategy, by comparing proportion of ‘proficient’ teachers, before and after an intervention. The number of teachers may differ between the two measurement time points, due to any number of reasons, and thus can result in an unequal number of observations in two periods. For such nonmatched design, we develop an adaptive Bayesian method, and suggest a heuristic decision procedure to conduct statistical inference. The authors use the -divergence measure to quantify the perturbation of the posterior distribution of the proportion in different time points. They present a simulation study to compare the statistical power between the adaptive Bayesian method and the existing frequents method. Their study and theoretical results indicate that under certain design, the adaptive Bayesian method outperforms the existing method. They administer the developed adaptive Bayesian method to two case studies.