HIV-1 viral fitness estimation using exchangeable on subsets priors and prior model selection

The phenotype-genotype problem is a fundamental problem of biology where an organism's genotype (genetic information) predicts its phenotype (observable characteristic). Viral fitness, defined as the reproductive capacity of a virus compared to a standard, is a continuous phenotype. We construct models to predict viral fitness as a function of mutation away from the standard wildtype virus. Data of this nature are difficult to analyse because there are potentially many more parameters than observations. We treat this issue as a regression problem using a prior with both a shrinkage component and a variable selection component. The key to practical implementation of the model is the prior specification for the regression coefficients. We use results from the scientific literature to construct several informative exchangeable within subsets priors (ESP). We use prior model selection (PMS) to select among our priors. Two novel graphics present results from five models each with 71 predictors.