It is crucial to check validation of any statistical model after fitting it for a given set of data. In Bayesian statistics, a researcher can check the fit of the model using a variety of strategies. In this paper we consider two major aspects, first checking that the posterior inferences are...

Many parameters and positive-definiteness are two major obstacles in estimating and modeling a correlation matrix for longitudinal data. In addition, when longitudinal data is incomplete, incorrectly modeling the correlation matrix often results in bias in estimating mean regression parameters....

Statistical modeling and inference problems with sample sizes substantially smaller than the number of available covariates are challenging. This is known as large p small n problem. Furthermore, the problem is more complicated when we have multiple correlated responses. We develop multivariate...

Markov basis for statistical model of contingency tables gives a useful tool for performing the conditional test of the model via the Markov chain Monte Carlo method. In this paper, we derive explicit forms of Markov bases for change point models and block diagonal effect models, which are...

Multidimensional scaling (MDS) is a technique which retrieves the locations of objects in a Euclidean space (the object configuration) from data consisting of the dissimilarities between pairs of objects. An important issue in MDS is finding an appropriate dimensionality underlying these...