17 : Markov Chain Monte

which decreases as J gets larger. So the approximation will be more accurate as we obtain more samples. Here is an example of using Monte Carlo methods to integrate away weights in Bayesian neural networks. Let y(x) = f(x,w) for response y and input x, and let p(w) be the prior over the weights w. The posterior distribution of w given the data D is p(w|D) ∝ p(D|w)p(w) where p(D|w) is the likelihood. For a test input x∗, we approximate the distribution of the response variable y∗ as