Further Inference on Categorical Data -- A Bayesian Approach

Three different inferential problems related to a two dimensional categorical data from a Bayesian perspective have been discussed in this article. Conjugate prior distribution with symmetric and asymmetric hyper parameters are considered. Newly conceived asymmetric prior is based on perceived preferences of categories. An extension of test of independence by introducing a notion of measuring association between the parameters has been shown using correlation matrix. Probabilities of different parametric combinations have been estimated from the posterior distribution using closed form integration, Monte-Carlo integration and MCMC methods to draw further inference from categorical data. Bayesian computation is done using R programming language and illustrated with appropriate data sets. Study has highlighted the application of Bayesian inference exploiting the distributional form of underlying parameters.