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Sampling from a Manifold

Persi Diaconis, Susan Holmes, and Mehrdad Shahshahani

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We develop algorithms for sampling from a probability distribution on a submanifold embedded in $\mathbb{R}^{n}$. Applications are given to the evaluation of algorithms in ‘Topological Statistics’; to goodness of fit tests in exponential families and to Neyman’s smooth test. This article is partially expository, giving an introduction to the tools of geometric measure theory.

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Galin Jones and Xiaotong Shen, eds., Advances in Modern Statistical Theory and Applications: A Festschrift in honor of Morris L. Eaton, (Beachwood, Ohio, USA: Institute of Mathematical Statistics, 2013) , 102-125

First available in Project Euclid: 23 September 2013

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Primary: 60K35: Interacting random processes; statistical mechanics type models; percolation theory [See also 82B43, 82C43] 60K35: Interacting random processes; statistical mechanics type models; percolation theory [See also 82B43, 82C43]
Secondary: 60K35: Interacting random processes; statistical mechanics type models; percolation theory [See also 82B43, 82C43]

manifold conditional distribution geometric measure theory sampling

Copyright © 2013, Institute of Mathematical Statistics


Diaconis, Persi; Holmes, Susan; Shahshahani, Mehrdad. Sampling from a Manifold. Advances in Modern Statistical Theory and Applications: A Festschrift in honor of Morris L. Eaton, 102--125, Institute of Mathematical Statistics, Beachwood, Ohio, USA, 2013. doi:10.1214/12-IMSCOLL1006.

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