Comparison of hit-and-run, slice sampler and random walk Metropolis
Keyword(s):
Abstract Different Markov chains can be used for approximate sampling of a distribution given by an unnormalized density function with respect to the Lebesgue measure. The hit-and-run, (hybrid) slice sampler, and random walk Metropolis algorithm are popular tools to simulate such Markov chains. We develop a general approach to compare the efficiency of these sampling procedures by the use of a partial ordering of their Markov operators, the covariance ordering. In particular, we show that the hit-and-run and the simple slice sampler are more efficient than a hybrid slice sampler based on hit-and-run, which, itself, is more efficient than a (lazy) random walk Metropolis algorithm.
2012 ◽
Vol 22
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pp. 881-930
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2018 ◽
Vol 28
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pp. 2966-3001
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2003 ◽
Vol 40
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pp. 123-146
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2003 ◽
Vol 40
(01)
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pp. 123-146
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2015 ◽
Vol 25
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pp. 2263-2300
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2019 ◽
Vol 55
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pp. 1599-1648
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2020 ◽
Vol 130
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pp. 297-327