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Markov Chain Monte Carlo Methods
Published on Feb 25, 200764911 Views
0. A fundamental theorem of simulation\\ 1. Markov chain basics\\ 2. Slice sampling\\ 3. Gibbs sampling\\ 4. Metropolis-Hastings algorithms\\ 5. Variable dimension models and reversible jump MCMC\\ 6.
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Chapter list
Monte Carlo Methods00:03
New [2004] edition:01:31
1 Introduction02:03
For a sample of...04:27
Likelihood of...05:24
Bayesian Methods06:38
Bayesian Methods (cont.)07:24
Posterior distribution central to Bayesian inference08:08
Example 2 –Binomial–08:21
A typology of Bayes computational problems09:30
Example 3 —Mixture of two normal distributions–16:53
Example 3 —Mixture of two normal distributions– (cont.)19:39
Bayes estimator20:35
Example 4 –AR(p) model–21:29
Integration over the parameters of all models23:39
Multiple layers of complexity24:36
Summary25:40
2. Monte Carlo Integration27:07
2.1 Classical Monte Carlo integration27:12
Accept-Reject Methods27:59
Fundamental theorem of simulation30:04
Accept-Reject method31:00
Validation of the Accept-Reject method32:51
Uniform repartition33:09
Two interesting properties34:41
Some intuitions35:29
Example 5 –Normal from a Cauchy–35:52
probability of acceptance ...36:13
Monte Carlo integration36:32
Monte Carlo integration (cont.)38:17
Example 6 –Cauchy prior–39:09
Example 6 –Cauchy prior– (cont.)40:50
Range of estimators42:01
2.2 Importance Sampling43:26