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### Sampling contingency tables

Martin Dyer, Ravi Kannan, John Mount
1997 Random structures & algorithms (Print)
Elements of I(r; c) are called contingency tables with these row and column sums. We consider two related problems on contingency tables.  ...  The random sampling problem is of interest in Statistics.  ...  Sampling Contingency tables : Reduction to continuous sampling This section reduces the problem of sampling from the discrete set of contingency tables to the problem of sampling with near-uniform density  ...

### Sampling Binary Contingency Tables

Ivona Bezáková
2008 Computing in science & engineering (Print)
The binary contingency tables problem has sparked the interest of statisticians and computer scientists alike.  ...  C o m b i n a t o r i c s I n C o m P U t i n G Sampling Binary Contingency Tables Ivona Bezáková Rochester Institute of Technology The binary contingency tables problem has sparked the interest of  ...  T he traditional motivation for the binary contingency tables problem comes from Charles Darwin.  ...

### Random Sampling of Contingency Tables via Probabilistic Divide-and-Conquer [article]

Stephen DeSalvo, James Y. Zhao
2016 arXiv   pre-print
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 technique.  ...  A simple exact sampling algorithm is presented for 2× n tables, as well as a generalization where each entry of the table has a specified marginal distribution.  ...  In this paper, we introduce new sampling algorithms for (r, c)-contingency tables.  ...

### Improved Bounds for Sampling Contingency Tables [chapter]

Ben Morris
1999 Lecture Notes in Computer Science
We study the problem of sampling contingency tables (nonnegative integer matrices with specified row and column sums) uniformly at random.  ...  This algorithm is based on a reduction to continuous sampling from a convex set. The same approach was taken by Dyer, Kannan, and Mount in previous work.  ...  ACKNOWLEDGMENTS I would like to thank Alistair Sinclair for telling me about the contingency tables problem and for many helpful conversations.  ...

### Improved bounds for sampling contingency tables

Ben J. Morris
2002 Random structures & algorithms (Print)
We study the problem of sampling contingency tables (nonnegative integer matrices with specified row and column sums) uniformly at random.  ...  This algorithm is based on a reduction to continuous sampling from a convex set. The same approach was taken by Dyer, Kannan, and Mount in previous work.  ...  ACKNOWLEDGMENTS I would like to thank Alistair Sinclair for telling me about the contingency tables problem and for many helpful conversations.  ...

### Negative Examples for Sequential Importance Sampling of Binary Contingency Tables [article]

Ivona Bezakova, Alistair Sinclair, Daniel Stefankovic, Eric Vigoda
2011 arXiv   pre-print
These are apparently the first theoretical results on the efficiency of the SIS algorithm for binary contingency tables.  ...  One of its noted applications is to the binary contingency tables problem, an important problem in statistics, where the goal is to estimate the number of 0/1 matrices with prescribed row and column sums  ...  contingency tables.  ...

### Characterizing Optimal Sampling of Binary Contingency Tables via the Configuration Model [article]

Jose Blanchet, Alexandre Stauffer
2011 arXiv   pre-print
The configuration model for uniformly sampling binary contingency tables proceeds as follows.  ...  Our finding shows surprising differences from recent results for binary symmetric contingency tables.  ...  to sampling a binary contingency table with different row and column sums.  ...

### Efficient importance sampling for binary contingency tables

Jose H. Blanchet
2009 The Annals of Applied Probability
As an illustration of our approach, we consider the problem of counting the number of binary tables with fixed column and row sums, c_j's and r_i's, respectively, and total marginal sums d=∑_jc_j.  ...  Importance sampling has been reported to produce algorithms with excellent empirical performance in counting problems.  ...  Liu for helpful discussions on contingency tables, to Dan Rudoy for valuable conversations on approximate counting, to Alistair Sinclair and Alexandre Stauffer for their very insightful comments on an  ...

### Sampling binary contingency tables with a greedy start

Ivona Bezáková, Nayantara Bhatnagar, Eric Vigoda
2006 Random structures & algorithms (Print)
We study the problem of counting and randomly sampling binary contingency tables.  ...  This is the first algorithm to directly solve binary contingency tables for all row/column sums.  ...  Conclusions We have presented an algorithm for directly solving binary contingency tables for arbitrary degree sequences.  ...

### Sampling binary contingency tables with a greedy start

Ivona Bezáková, Nayantara Bhatnagar, Eric Vigoda
2006 Proceedings of the seventeenth annual ACM-SIAM symposium on Discrete algorithm - SODA '06
We study the problem of counting and randomly sampling binary contingency tables.  ...  This is the first algorithm to directly solve binary contingency tables for all row/column sums.  ...  Conclusions We have presented an algorithm for directly solving binary contingency tables for arbitrary degree sequences.  ...

### Tables for Use with Binomial Samples—Contingency Tests, Confidence Limits and Sample Size Estimates

1957 Forest Science
Tables for Use with Binomial SamplesContingency Tests, Confidence Limits and Sample Size Estimates By Donald Mainland, Lee Herrera and Marion I, Sutcliffe.  ...  The tables comprise three groups: (1) Tables I-IV are for the significance testing of fourfold contingency tables. For samples up to size 20, exact probabilities are given.  ...

### A discussion on significance indices for contingency tables under small sample sizes

Natalia L. Oliveira, Carlos A. de B. Pereira, Marcio A. Diniz, Adriano Polpo, Mauro Gasparini
2018 PLoS ONE
Hypothesis testing in contingency tables is usually based on asymptotic results, thereby restricting its proper use to large samples.  ...  The exact Fisher test for 2 × 2 tables that drastically reduces the sample space is also discussed.  ...  1 . 1 Contingency table 2 × 2.  ...

### Random sampling of Latin squares via binary contingency tables and probabilistic divide-and-conquer [article]

Stephen DeSalvo
2017 arXiv   pre-print
The algorithm divides the entries of the table modulo powers of 2, and samples a corresponding binary contingency table at each level.  ...  The sampling distribution is based on the Boltzmann sampling heuristic, along with probabilistic divide-and-conquer.  ...  , contingency tables.  ...

### Two-Sample Tests that are Safe under Optional Stopping, with an Application to Contingency Tables [article]

Rosanne Turner, Alexander Ly, Peter Grünwald
2021 arXiv   pre-print
We illustrate the generic construction through the special case of 2x2 contingency tables, where we also allow for the incorporation of different restrictions on a composite alternative.  ...  These E variables lead to tests that remain safe, i.e. keep their Type-I error guarantees, under flexible sampling scenarios such as optional stopping and continuation.  ...  While our tests can be implemented for arbitrary {P θ : θ ∈ Θ}, we extensively illustrate them on a simple, classical problem: 2 × 2 contingency tables.  ...

### Polynomial Time Perfect Sampling Algorithm for Two-Rowed Contingency Tables [chapter]

Shuji Kijima, Tomomi Matsui
2004 Mathematics and Computer Science III
This paper proposes a polynomial time perfect (exact) sampling algorithm for 2 × n contingency tables.  ...  The algorithm is based on monotone coupling from the past (monotone CFTP) algorithm and new Markov chain for sampling two-rowed contingency tables uniformly.  ...  There are many works for almost uniform sampling contingency tables using a Markov chain.  ...
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