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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.