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Activity Number:
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257
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Type:
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Contributed
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Date/Time:
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Tuesday, August 13, 2002 : 2:00 PM to 3:50 PM
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Sponsor:
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Section on Statistical Computing*
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| Abstract - #301049 |
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Title:
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An Efficient Markov Chain Monte Carlo Proposal Distribution for Ridgelike Target Distributions Using Nearest Neighbors
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Author(s):
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Samantha Bates*+ and Adrian Raftery
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Affiliation(s):
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Virginia Polytechnic Institute and State University and University of Washington
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Address:
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Hutcheson Hall (0439), Blacksburg, Virginia, 24061, USA
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Keywords:
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Bayesian Inference ; Deterministic Models ; Markov chain Monte Carlo ; Metropolis-Hastings algorithm ; Nearest Neighbors ; Sampling Importance Resampling
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Abstract:
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We develop a Markov chain Monte Carlo (MCMC) proposal distribution for exploring distributions which lie on a ridge in relatively high dimensional space. One context in which these ridgelike distributions may occur is in posterior distributions for inputs and/or outputs of deterministic models. The proposal distribution we present is a multivariate normal proposal distribution based on the nearest neighbors of the current state in a pilot sample. This proposal distribution adapts to the shape of the (unknown) posterior but still satisfies the ergodicity property. We present a simulated example in which MCMC with this nearest neighbor proposal outperforms generic MCMC methods and the sampling importance resampling approach of Rubin (1988) in terms of the number of model runs required for a given number of approximately independent draws from the posterior distribution. Further, we present simulation results which suggest a good choice of covariance multiplier in these cases.
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