1. Markov Chain Monte Carlo
10701 Recitation
Pengtao Xie
1/17/2019

2. Outline Sampling Methods Rejection Sampling Importance Sampling
MCMC Sampling
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3. Outline Sampling Methods Rejection Sampling Importance Sampling
MCMC Sampling
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4. How to represent a distribution
Closed form representation
Gaussian distribution, Dirichlet distribution, Multinomial distribution
Sample based representation
Draw samples from the distribution and use samples to compute expectation, variance, etc
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5. Outline Sampling Methods Rejection Sampling Importance Sampling
MCMC Sampling
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6. May reject a lot of samples
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7. Outline Sampling Methods Rejection Sampling Importance Sampling
MCMC Sampling
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8. Importance sampling
Drawback: hard to find a Q which matches well with P, may give little importance to most samples
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9. Outline Sampling Methods Rejection Sampling Importance Sampling
MCMC Sampling
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10. Markov Chain Monte Carlo Sampling
Motivation
In rejection sampling and importance sampling, Q is fixed. May reject or give little importance to most samples
Idea
Use an adaptive Q
Methods
Metropolis-Hastings
Gibbs sampling
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24. Is distribution Q adaptive?
Summary
Is distribution Q adaptive? NO
YES
Is accept rate 1?
Is accept rate 1? NO
YES NO
YES
Rejection
Sampling
Importance
Sampling MH
Gibbs
Sampling
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25. References Slides courtesy MCMC theory
Professor Eric Xing, Graphical Models
MCMC theory
Slides 15-21
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