Model comparisons and predictive mean computations for hierarchical Bayesian neural nets: quadratic approximation vs. MCMC

The article is a first step toward an attempt to demonstrate the validity of quadratic approximations (QAP) of computing marginal likelihood as well as predictive distributions for the hierarchical Bayesian scheme by using MCMC (Markov chains Monte Carlo). At least for the simple examples considered, the QAP gives reasonable results for marginal likelihood and predictive distributions. More elucidation is necessary to further study the issues for more complicated problems including nonlinear time series prediction problems.