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Activity Number:
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80
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Type:
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Contributed
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Date/Time:
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Monday, August 9, 2004 : 8:30 AM to 10:20 AM
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Sponsor:
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Section on Statistical Computing
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| Abstract - #302128 |
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Title:
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First Hitting Time Analysis of the Independence Metropolis Sampler
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Author(s):
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Romeo Maciuca*+ and Song-Chun Zhu
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Companies:
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University of California, Los Angeles and University of California, Los Angeles
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Address:
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8130 Math Sciences Bldg., Los Angeles, CA, 90095-1554,
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Keywords:
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fundamental matrix ; Metropolized Gibbs Sampler ; Independence Metropolis Sampler ; eigenanalysis ; expectation ; variance
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Abstract:
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The focus of the presentation will be a special case of the Metropolis algorithm, the Independence Metropolis Sampler (IMS), for finite state spaces. The IMS is often used in designing components of more complex Markov chain Monte Carlo algorithms. We present new results related to the first hitting time of individual states for the IMS. These results are expressed mostly in terms of the eigenvalues of the transition kernel. We derive a simple form formula for the mean first hitting time and we show tight lower and upper bounds on the mean first hitting time with the upper bound being the product of two factors: a "local" factor corresponding to the target state and a "global" factor, common to all the states, which is expressed in terms of the total variation distance between the target and the proposal probabilities. We also briefly discuss properties of the distribution of the first hitting time for the IMS and analyze its variance. We conclude by showing how nonindependence Metropolis-Hastings algorithms can perform better than the IMS.
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