Journal Article10.1002/RSA.20087
Polynomial time perfect sampling algorithm for two-rowed contingency tables
Shuji Kijima,Tomomi Matsui +1 more
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TL;DR: The result indicatesthat uniform generation of two-rowed contingency tables is easier than the corresponding counting problem, since the counting problem is known to be #P-complete.
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Abstract: This paper proposesapolynomialtime perfect (exact)sampling algorithm for2 xn contingencytables.Our algorithm isa LasVegas type randomized algorithm and the expected running time is boundedby 0(n3InN) where n isthenumber of columnsandN is the total sum of whole entries ina table.The algorithm is based on monotone coupling from thepast(monotone CFTP) algorithm and new Markov chain for sampling two-rowed contingency tables uniformly. We employed thepathcoupling methodandshowed the mixing rate of our chain. Our result indicatesthatuniform generation of two-rowed contingency tables is easier than the corresponding counting problem,since the counting problem is known to be #P-complete.
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Citations
Randomized approximation scheme and perfect sampler for closed Jackson networks with multiple servers
Shuji Kijima,Tomomi Matsui +1 more
TL;DR: In this paper, the authors proposed a fully polynomial-time randomized approximation scheme (FPRAS) for a closed Jackson network, which is based on the Markov chain Monte Carlo (MCMC) method.
9
Phase-II Monitoring and Diagnosing of Multivariate Categorical Processes Using Generalized Linear Test Based Control Charts
TL;DR: Two control charts based on the generalized linear test (GLT) and contingency table are proposed for Phase-II monitoring of multivariate categorical processes and a new scheme is proposed to identify the parameter responsible for an out-of-control signal.
8
Approximation Algorithm and Perfect Sampler for Closed Jackson Networks with Single Servers
Shuji Kijima,Tomomi Matsui +1 more
TL;DR: This paper proposes the first fully polynomial-time randomized approximation scheme (FPRAS) for closed Jackson networks with single servers based on the Markov chain Monte Carlo method, and proposes two Markov chains for approximate sampling and perfect sampling.
7
New Approaches in Monitoring Multivariate Categorical Processes based on Contingency Tables in Phase II
TL;DR: Two new control charts based on the WALD and Stuart score test statistics are designed for monitoring of contingency table-based processes in Phase-II and are proposed to improve the performance of Shewhart-based control charts in detecting small and moderate shifts in contingency table parameters.
7
•Posted Content
Random Sampling of Contingency Tables via Probabilistic Divide-and-Conquer
Stephen DeSalvo,James Y. Zhao +1 more
TL;DR: 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 is presented, and a generalization to the sampling algorithm where each entry of the table has a specified marginal distribution.
7
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