Lecture on Stochastic Simulation Methods for Probabilistic Inference

Abstract

Technique for approximate inference in Bayesian networks • Run repeated simulations of the world described by the network • Estimate the probabilities we are interested in by counting the frequencies with which relevant events occur Get probabilities from samples • If we could sample from a variable's posterior probability, we could estimate its posterior probability • Probabilities correspond to samples 2 Estimating Probabilities: An Example Suppose we wish to estimate the probability p that a certain drawing pin lands heads. We toss it 100 times and it comes up heads 35 times. What is our best guess for p? If we had tossed it once, and it had come up heads, what would be our guess for p then? 3 The Law of the Large Numbers Consider tossing a coin a large number of times, where the probability of heads on any toss is p. Let Sn be the number of heads that come after n tosses. Think of Sn as the number of successes The law of large numbers says that the probability that Sn n differs much from p becomes smaller and smaller as n gets bigger If ɛ> 0, then as n → ∞ it holds P ( | Sn n − p | < ɛ) →