Bayesian modeling of binomial experiments in sociology: problem analysis

Abstract

The article is devoted to Bayesian modeling of simple comparative binomial experiments with binary data sets (of “hit” and “miss” format) in sociology and other social sciences. The main methodological foundations of application of Bayesian approach in statistics are briefly reviewed: the use of priors in analysis, features of Bayesian statistical inference, differences in frequency and Bayesian confidence intervals, features of hypothesis testing in Bayesian statistics. A Bayesian model of a comparative binomial experiment has been constructed. It supports comparison of independent and dependent samples of binomial variables, and also allows for differences in sizes of the compared samples. The capabilities of the model, as well as the principles of the Bayesian hypothesis testing, were demonstrated on test data using PyMC and ArviZ, contemporary free packages of the Bayesian modeling and analysis. The use of these tools allows implementing direct tensor operations with the obtained posterior distributions and provides the researcher with an effective way to calculate the effect size when comparing two binomial samples without having to resort to complicated forms of calculating this parameter. The possibilities and limitations of the Bayesian approach are shown in the context of comparative analysis of the results of binomial experiments in social sciences by estimating the probability of hypotheses via finding and comparing the area of intervals of posterior distributions