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A fast MCMC algorithm for the uniform sampling of binary matrices with fixed margins. (English) Zbl 1439.62060

Summary: Uniform sampling of binary matrix with fixed margins is an important and difficult problem in statistics, computer science, ecology and so on. The well-known swap algorithm would be inefficient when the size of the matrix becomes large or when the matrix is too sparse/dense. Here we propose the Rectangle Loop algorithm, a Markov chain Monte Carlo algorithm to sample binary matrices with fixed margins uniformly. Theoretically the Rectangle Loop algorithm is better than the swap algorithm in Peskun’s order. Empirical studies also demonstrate that the Rectangle Loop algorithm is remarkably more efficient than the swap algorithm.

MSC:

62D05 Sampling theory, sample surveys
62-08 Computational methods for problems pertaining to statistics
62H12 Estimation in multivariate analysis
65C05 Monte Carlo methods
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