Bayesian and Akaike’s information criterions for some multivariate tests of homogeneity with applications in multisample clustering

Abstract

W pracy zostały przedstawione dwa kryteria dotyczące selekcji modeli, mianowicie kryterium Akaike: AIC (Akaike’s Information Criterion) i kryterium bayesowskie: BIC (Bayesian Information Criterion).

This paper studies the AlC and B1C (Akaike’s and Bayesian Information Criterion) replacement for: - Box’s (1949) M test of the homogeneity of covariances, - Wilks’ (1932) Л criterion for testing the equality of mean vectors and - likelihood ratio test of the complete homogeneity as two of model - selection criterions. AIC and BIC are new procedures for comparing means and samples, and selecting the homogeneous groups from heterogenous ones in multi-sample data analysis problems. f rom the Bayesian view-point, the approach to the model-selection problem is to specily the prior probability ol each model, prior distributions for all parameters in each model and compute the posterior probability of each model given the data. That model lor which the estimated posterior probability is the largest is chosen to be the best one. A clustering technique is presented to generate all possible choices of clustering alternatives of groups and indentify the best clustering among the alternative clusterings.