Neural network approximations to posterior densities: an analytical approach

Abstract

In Hoogerheide, Kaashoek and Van Dijk (2002) the class of neural networksampling methods is introduced to sample from a target (posterior)distribution that may be multi-modal or skew, or exhibit strong correlationamong the parameters. In these methods the neural network is used as animportance function in IS or as a candidate density in MH. In this note wesuggest an analytical approach to estimate the moments of a certain (target)distribution, where `analytical' refers to the fact that no samplingalgorithm like MH or IS is needed.We show an example in which our analyticalapproach is feasible, even in a case where a `standard' Gibbs approach wouldfail or be extremely slow.Markov chain Monte Carlo;Bayesian inference;importance sampling;neural networks