Bayesian estimation procedures often require Monte Carlo integration with respect to the posterior distribution. We propose a Monte Carlo estimator of an arbitrary posterior-distribution property, as well as its gradient with respect to prior-distribution hy-perparameters and to the observed data. Unlike most Monte Carlo samplers for Bayesian problems, we sample from the prior distribution, which is usually more tractable than the posterior distribution. We discuss sufficient conditions for interchanging expected value and differentiation, so that the gradient can be estimated by averaging observations of the stochastic gradient. In addition to the gradient estimator, we suggest asymptotically valid standard error and confidence-interval estimators. We give two numerical examples.
['Jin Wang', 'Bruce W. Schmeiser']
Monte Carlo estimation of Bayesian robustness