In Hoogerheide, Kaashoek and Van Dijk (2002) the class of neural network sampling methods is introduced to sample from a target (posterior) distribution that may be multi-modal or skew, or exhibit strong correlation among the parameters. In these methods the neural network is used as an importance function in IS or as a candidate density in MH. In this note we suggest an analytical approach to estimate the moments of a certain (target) distribution, where `analytical' refers to the fact that no sampling algorithm like MH or IS is needed.We show an example in which our analytical approach is feasible, even in a case where a `standard' Gibbs approach would fail or be extremely slow.

Bayesian inference, Markov chain Monte Carlo, importance sampling, neural networks
Econometric Institute Research Papers
Erasmus School of Economics

Hoogerheide, L.F, Kaashoek, J.F, & van Dijk, H.K. (2003). Neural network approximations to posterior densities: an analytical approach (No. EI 2003-38). Econometric Institute Research Papers. Retrieved from