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A general framework for approximate sampling with an application to generating points on the boundary of bounded convex regions

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  • H. E. Romeijn

Abstract

We consider the problem of generating a sample of points according to some given probability distribution over some region. We give a general framework for constructing approximate sampling algorithms based on the theory of Markov chains. In particular, we show how it can be proven that a Markov chain has a limiting distribution. We apply these results to prove convergence for a class of so‐called Shake‐and‐Bake algorithms, which can be used to approximate any absolutely continuous distribution over the boundary of a full‐dimensional convex body.

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  • H. E. Romeijn, 1998. "A general framework for approximate sampling with an application to generating points on the boundary of bounded convex regions," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 52(1), pages 42-59, March.
    • Handle: RePEc:bla:stanee:v:52:y:1998:i:1:p:42-59
    DOI: 10.1111/1467-9574.00067
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    Cited by:

    1. A. B. Dieker & Santosh S. Vempala, 2015. "Stochastic Billiards for Sampling from the Boundary of a Convex Set," Mathematics of Operations Research, INFORMS, vol. 40(4), pages 888-901, October.

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