# Download American Mathematical Monthly, volume 117, May 2010 by Daniel J. Velleman PDF

By Daniel J. Velleman

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Smith and G. O. Roberts, Bayesian computation via the Gibbs sampler and related Markov chain Monte Carlo methods, J. Roy. Statist. Soc. Ser. B 55 (1993) 3–23. 60. R. Swendsen and J. Wang, Nonuniversal critical dynamics in Monte Carlo simulations, Phys. Rev. Lett. 58 (1987) 86–88. 86 61. M. Tanner, Tools for Statistical Inference: Methods for Exploration of Posterior Distributions and Likelihood Functions, Springer-Verlag, New York, 1993. 62. M. Tanner and W. Wong, The calculation of posterior distributions by data augmentation, J.

For a positive integer p, the symbol p− in a cell indicates that the cell contains a positive integer less than or equal to p. Similarly, the symbol p+ indicates that the integer in the cell is greater than or equal to p. Theorem 1. If n is less than (k + 2)/2, then a k-by-n array in which each column has k distinct integers has a transversal (of length n). Proof. We proceed by induction on n. Clearly the theorem is true for n = 1. Now assume that it is true for n, and consider a k-by-(n + 1) array in which each column has k distinct integers and n + 1 < (k + 2)/2.

J. Kirby, Gibbs sampling in medicine, J. Roy. Statist. Soc. Ser. B 55 (1993) 39–52. 30. W. R. Gilks, S. Richardson, and D. J. Spiegelhalter, Markov Chain Monte Carlo in Practice, Chapman & Hall/CRC, London, 1996. 31. R. Glauber, Time dependent statistics of the Ising model, J. Math. Phys. 4 (1963) 294–307. doi:10. 1703954 32. J. E. Gubernatis, Marshall Rosenbluth and the Metropolis algorithm, Phys. Plasmas 12 (2005) 1–5. 1887186 33. A. Habibi, Two-dimensional Bayesian estimate of images, Proceedings of the IEEE 60 (1972) 878–883.