A1225
Title: An efficient Bayesian MCMC for nonlinear hierarchical models: Computation of marginal likelihood
Authors: Emi Mise - University of Leicester (United Kingdom) [presenting]
James Cannam - University of Leicester (United Kingdom)
Abstract: Bayesian hierarchical models are becoming increasingly popular due to increasing computer power and availability of data in fields as diverse as medicine, economics, and psychology. The focus is on presenting an efficient method of retrieving posterior densities in a nonlinear hierarchical model in which the structural parameters of interest are a complex nonlinear function of the natural parameters of the statistical model. Survival analysis and decision theories fall into this category. In this case, the standard MCMC algorithm is either enormously computationally expensive or impossible to implement in practice, as the dimension of the parameter space grows exponentially as the number of participants increases. Using two decision theories, stochastic cumulative prospect theory (CPT) and decision by sampling (DbS), as examples, an efficient two-stage estimation method is presented. It is shown that this gives a substantial computational advantage by enabling parallel computing. The simulation results demonstrate that this method works well for both CPT, whose parameters of interest are all continuous and thus can be transformed to the entire real line, and for DbS, which has a mix of continuous and discrete parameters. In addition, data from over 560 subjects shows that DbS has some serious shortcomings despite its early promise. The mechanism is also extended to enable an efficient computation of the marginal likelihoods of competing models.
