A general framework for approximate sampling with an application to generating points on the boundary of bounded convex regions[Note 1. This material is based on work supported by a ...] | Zendy

Romeijn H. E. | Zendy

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A general framework for approximate sampling with an application to generating points on the boundary of bounded convex regions[Note 1. This material is based on work supported by a ...]

Author(s) -

Romeijn H. E.

Publication year - 1998

Publication title -

statistica neerlandica

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.52

H-Index - 39

eISSN - 1467-9574

pISSN - 0039-0402

DOI - 10.1111/1467-9574.00067

Subject(s) - mathematics , markov chain , bounded function , boundary (topology) , regular polygon , convergence (economics) , distribution (mathematics) , sampling (signal processing) , class (philosophy) , mathematical optimization , mathematical analysis , computer science , statistics , geometry , filter (signal processing) , artificial intelligence , economics , computer vision , economic growth

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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