Stemming from work by Buntine and Weigend (1991) and MacKay (1992), th
ere is a growing interest in Bayesian analysis of neural network model
s. Although conceptually simple, this problem is computationally invol
ved. We suggest a very efficient Markov chain Monte Carlo scheme for i
nference and prediction with fixed-architecture feedforward neural net
works. The scheme is then extended to the variable architecture case,
providing a data-driven procedure to identify sensible architectures.