Comparação bayesiana de modelos com uma aplicação para o equilíbrio de Hardy-Weinberg usando o coeficiente de desequilíbrio

Abstract

One of the main subjects studied by population genetics is the Hardy-Weinberg equilibrium. In this context, this paper addresses the analysis and comparison of bayesian models used in its evaluation by the coefficient of disequilibrium. For this, it was carried out a simulation study in which the following prior distributions were considered: Dirichlet (model 1), beta - uniform step function (model 2), uniform - uniform step function (model 3) and independent uniform priors (model 4). Examples of application to real data for racial groups are presented and discussed. Samples from the marginal posterior distributions for parameters of interest were obtained by Metropolis-Hastings algorithm, which was implemented in the software R. The convergence of the chains generated by this algorithm was monitored by criteria of Geweke and Gelman & Rubin, which are implemented in the BOA package R. Regarding comparisons between models, performed using the Bayes factor, it was observed that model 4 is the most suitable for the cases of DA=0.146, DA=0.02 and DA=-0.02 with n=200, the model 2 is the most suitable for DA=-0.02 with n=50 and the model 3 is the most suitable for DA=-0.02 and n=1000. For real data, in each case examined, there is a large difference in choice of models, where model 1 is the only one not recommended.