Random sampling of contingency tables via probabilistic divide-and-conquer
We present a new approach for random sampling of contingency tables of any size and constraints based on a recently introduced probabilistic divide-and-conquer (PDC) technique. Our first application is a recursive PDC: it samples the least significant bit of each entry in the table, motivated by the...
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| Published in: | Computational statistics Vol. 35; no. 2; pp. 837 - 869 |
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| Main Authors: | , |
| Format: | Journal Article |
| Language: | English |
| Published: |
Berlin/Heidelberg
Springer Berlin Heidelberg
01.06.2020
Springer Nature B.V |
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| ISSN: | 0943-4062, 1613-9658 |
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| Abstract | We present a new approach for random sampling of contingency tables of any size and constraints based on a recently introduced
probabilistic divide-and-conquer
(PDC) technique. Our first application is a recursive PDC: it samples the least significant bit of each entry in the table, motivated by the fact that the bits of a geometric random variable are independent. The second application is via PDC deterministic second half, where one divides the sample space into two pieces, one of which is deterministic conditional on the other; this approach is highlighted via an exact sampling algorithm in the
2
×
n
case. Finally, we also present a generalization to the sampling algorithm where each entry of the table has a specified marginal distribution. |
|---|---|
| AbstractList | We present a new approach for random sampling of contingency tables of any size and constraints based on a recently introduced
probabilistic divide-and-conquer
(PDC) technique. Our first application is a recursive PDC: it samples the least significant bit of each entry in the table, motivated by the fact that the bits of a geometric random variable are independent. The second application is via PDC deterministic second half, where one divides the sample space into two pieces, one of which is deterministic conditional on the other; this approach is highlighted via an exact sampling algorithm in the
2
×
n
case. Finally, we also present a generalization to the sampling algorithm where each entry of the table has a specified marginal distribution. We present a new approach for random sampling of contingency tables of any size and constraints based on a recently introduced probabilistic divide-and-conquer (PDC) technique. Our first application is a recursive PDC: it samples the least significant bit of each entry in the table, motivated by the fact that the bits of a geometric random variable are independent. The second application is via PDC deterministic second half, where one divides the sample space into two pieces, one of which is deterministic conditional on the other; this approach is highlighted via an exact sampling algorithm in the 2×n case. Finally, we also present a generalization to the sampling algorithm where each entry of the table has a specified marginal distribution. |
| Author | DeSalvo, Stephen Zhao, James |
| Author_xml | – sequence: 1 givenname: Stephen surname: DeSalvo fullname: DeSalvo, Stephen email: stephendesalvo@gmail.com organization: UCLA Department of Mathematics – sequence: 2 givenname: James surname: Zhao fullname: Zhao, James organization: USC Department of Mathematics |
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| Cites_doi | 10.2307/2331961 10.1080/15427951.2010.557277 10.1007/s11222-009-9115-1 10.1016/j.aam.2017.06.005 10.1016/j.aim.2006.07.012 10.1002/rsa.20087 10.1137/S0097539703434243 10.1017/S0963548307008668 10.1093/imrn/rnn133 10.1080/10618600.2012.680369 10.1017/S0963548310000039 10.1198/016214504000001303 10.1006/aima.1994.1022 10.1002/rsa.10049 10.1016/0012-365X(74)90118-6 10.1016/0012-365X(77)90117-0 10.1002/(SICI)1098-2418(199608/09)9:1/2<223::AID-RSA14>3.0.CO;2-O 10.1007/s10208-003-0088-8 10.1093/biomet/19.3-4.225 10.1145/102782.102783 10.1016/j.jspi.2011.10.010 10.1080/0308108031000098450 10.1137/040610623 10.1016/j.jsc.2003.04.003 10.1016/S0022-0000(03)00014-X 10.1007/978-1-4613-8643-8 10.1016/j.aam.2010.01.004 10.1090/S0002-9947-2012-05585-1 10.1017/S0963548304006315 10.1214/009053605000000822 10.1017/S0963548315000358 10.1016/j.tcs.2004.06.014 10.1002/rsa.20301 10.1016/S0304-3975(99)00136-X 10.1016/j.aam.2008.01.002 10.1214/aos/1030563990 10.1007/978-1-4612-0801-3_3 10.1007/11841036_15 10.1109/WSC.2011.6147745 |
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probabilistic divide-and-conquer... We present a new approach for random sampling of contingency tables of any size and constraints based on a recently introduced probabilistic divide-and-conquer... |
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| SubjectTerms | Algorithms Contingency Contingency tables Economic Theory/Quantitative Economics/Mathematical Methods Mathematics and Statistics Monte Carlo simulation Original Paper Probability and Statistics in Computer Science Probability theory Probability Theory and Stochastic Processes Random sampling Random variables Sampling techniques Statistics |
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| Title | Random sampling of contingency tables via probabilistic divide-and-conquer |
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