Introduction: Metropolis-Hasting Sampler Purpose--To draw samples from a probability distribution There are three steps 1Propose a move from x to y 2Accept.

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Presentation transcript:

Introduction: Metropolis-Hasting Sampler Purpose--To draw samples from a probability distribution There are three steps 1Propose a move from x to y 2Accept the move from x to y 3. Move from x to y

Detailed Balance Equations Rate from x to y Rate from y to x

Detailed Balance Equation

When is Metropolis-Hasting Sampler useful? No explicit formula for Yet the likelihood ratio has an explicit formula

Example 1 Bayesian Posterior

Frequency Statistics Suppose that the likelihood of Where are latent variables Use MCMC to simulate Then

switched with 2

Importance Sampling

Sample from the proposal distribution Importance Sampling

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