Statistical Analysis With a Bayesian Approach to the Hardy-Weinberg Equilibrium

Abstract

In population genetics, it is very common to use statistical analysis to test the Hardy-Weinberg genetic equilibrium in a given population. The classical method of approaching this problem is done through the chi-square test that often leads to the verification of the equilibrium hypothesis. In the present work, a Bayesian analysis was developed involving hypothesis testing, estimation and credibility intervals to test this balance. Data on M, MN and N blood groups from the MNS system were used on samples from two populations, one from Brazilians and one from North Americans, obtained by Beiguelman (1977). The HardyWeinberg equilibrium adhesion chi-square test was performed, where the acceptance of the Hardy-Weinberg equilibrium hypothesis was confirmed. By Bayesian analysis, the rejection of the Hardy-Weinberg equilibrium hypothesis was confirmed, mainly by the Bayes factor. Our primary concern was to develop a Bayesian technique as an alternative to testing HardyWeinberg equilibrium using the MNSs blood sample data. The result obtained may encourage researchers mainly in the field of biological sciences to practice Bayesian Methodology, as an alternative in statistical tests.