Bayesian model calibration and uncertainty quantification for an HIV model using adaptive Metropolis algorithms

Abstract

In this paper, we discuss Bayesian model calibration and use adaptive Metropolis algorithms to construct densities for input parameters in a previously developed HIV model. To quantify the uncertainty in the parameters, we employ two MCMC algorithms: Delayed Rejection Adaptive Metropolis (DRAM) and Differential Evolution Adaptive Metropolis (DREAM). The densities obtained using these methods are compared to those obtained through direct evaluation of Bayes formula. We also employ uncertainties in input parameters and observation errors to construct prediction intervals for a model response. We verify the accuracy of the Metropolis algorithms by comparing chains, densities and correlations obtained using DRAM, DREAM and direct numerical evaluation of Bayes’ formula. We also perform similar analysis for credible and prediction intervals for responses.