Assessment of Deleterious Gene Models Using Predictive p-values

Abstract

Using both hierarchical modeling and Bayesian computing techniques, Lee, Newton, Nordheim and Kang (1994) proposed a complex statistical model for studying the characteristics of deleterious genes in plant species. To assess the fit of such models the use of posterior predictive checks has been suggested. These techniques are based on measures of the discrepancy between the observed data and potential data evaluated with respect to the posterior predictive distribution. In our current study we use a posterior predictive p-value, evaluating the probability of observing a predictive density as small as that actually observed. To calculate these posterior predictive p-values from the sample output of the predictive distribution, we use both a density estimation technique and a quantile method. Because we avoid the difficulties of evaluating this p-value directly from the posterior predictive distribution and because our evaluation of the p-value does not rely on any discrepancy measures, it is straightforward in our case. Regarding the assumption about a genetic parameter representing intensity of mortality of deleterious genes, our results indicate a better fit of a mildly-deleterious model as compared with strongly-deleterious or full lethal models.