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Activity Number:
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405
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Type:
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Topic Contributed
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Date/Time:
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Wednesday, August 6, 2003 : 2:00 PM to 3:50 PM
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Sponsor:
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Section on Bayesian Stat. Sciences
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| Abstract - #300157 |
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Title:
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BMM: A Simple, General Algorithm for Drawing from Densities
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Author(s):
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Robert E. McCulloch*+ and Xiao-Li Meng and John Barnard
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Companies:
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University of Chicago and Harvard University and DeCODE Genetics
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Address:
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1101 East 58th St., Chicago, IL, 60637-1511,
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Keywords:
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random variate generation ; simulation ; Monte-Carlo ; Metropolis algorithm ; binary search ; bivariate distribution
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Abstract:
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We propose a simple and general approach for drawing from a probability distribution represented by a density. We focus on drawing from a bivariate density, but in principle, the method could be used in any dimension. All that the method assumes is that we are able to evaluate the density. The method is based on the Metropolis algorithm. The Metropolis algorithm works by accepting candidate draws in such a way that the stationary distribution of the resulting sequence of draws is the one we want. The key is our approach for generating candidate draws. We divide the support of the distribution into disjoint regions. Within each region, we evaluate the density at strategically chosen locations. One of the regions is stochastically chosen in such a way that a region where the density evaluations are larger is more likely to be chosen. We then iterate by partitioning the chosen region and repeating the process. We continue partitioning and choosing subregions until only a small region is left and then draw from this region (e.g uniformly). This draw is then used as the candidate in the Metropolis algorithm.
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