Stochastic Approximations (cont.)

How do we sample from P(?|D)?

Markov Chain Monte Carlo (MCMC) methods:

• Find a Markov Chain whose stationary probability Is P(?|D)

• Simulate the chain until convergence to stationary behavior

• Collect samples for the “stationary” regions

Pros:

• Very flexible method: when other methods fails, this one usually works

• The more samples collected, the better the approximation

Cons:

• Can be computationally expensive

• How do we know when we are converging on stationary distribution?

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