Models such as feed-forward neural networks and certain other structures investigated in the computer science literature are not amenable to closed-form Bayesian analysis. The paper reviews the various approaches taken to overcome this difficulty, involving the use of Gaussian approximations, Markov chain Monte Carlo simulation routines and a class of non-Gaussian but “deterministic” approximations called variational approximations.
"Bayesian Methods for Neural Networks and Related Models." Statist. Sci. 19 (1) 128 - 139, February 2004. https://doi.org/10.1214/088342304000000099