A Study of the discrepancy function when modeling a packed bed using Variational Bayes and Gaussian processes

Abstract

Estimating properties using maximum likelihood (MLE) gives point values and a rough idea of the uncertainty in the parameters if their distributions are approximately normal. More accurate results require a Monte Carlo approach, often using the Markov Chain Monte Carlo (MCMC) method, which for complex models is unrealistic because of the computational expense. The Variational Bayes approach gives results comparable to MCMC with only a few evaluation of the model. When the model is imprecise or expensive to evaluate, Gaussian processes provide one means of analyzing the noise to determine the uncertainties.