Orbit-based conditional tests. A link between permutations and Markov bases

Algebraic sampling methods are a powerful tool to perform hypothesis testing for non-negative discrete exponential families, when the exact computation of the test statistic null distribution is computationally infeasible. We propose an improvement of the accelerated sampling described by Diaconis a...

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Bibliographic Details
Published in:Journal of statistical planning and inference 2020-03, Vol.205, p.23-33
Main Authors: Fontana, Roberto, Crucinio, Francesca Romana
Format: Article
Language:English
Subjects:
Algebraic statistics
Conditional test
Discrete exponential family
Markov chain Monte Carlo
Permutation test
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Summary:Algebraic sampling methods are a powerful tool to perform hypothesis testing for non-negative discrete exponential families, when the exact computation of the test statistic null distribution is computationally infeasible. We propose an improvement of the accelerated sampling described by Diaconis and Sturmfels (1998) based on permutations. We thus establish a link between standard permutation and algebraic-statistics-based sampling. We prove that the permutations-based sampling gives the lowest approximation errors and we validate our algorithm through a simulation study on three applications (data fitting, two sample tests and linear regression). •Conditional hypothesis testing for non-negative discrete exponential families can be speed up using orbits of permutations.•A theoretical link between standard permutation and algebraic statistics-based sampling is established.•The range of application of the method includes data fitting, two-sample tests and linear regression.
ISSN:0378-3758
1873-1171
DOI:10.1016/j.jspi.2019.05.007