We construct Markov chain algorithms for sampling from discrete exponential families conditional on a sufficient statistic. Examples include generating tables with fixed row and column sums and higher dimensional analogs. The algorithms involve finding bases for associated polynomial ideals and so an excursion into computational algebraic geometry.

A procedure is proposed for approximating attained significance levels of exact conditional tests. The procedure utilizes a sampling from the null distribution of tables having the same marginal frequencies as the observed table. Application of the approximation through a computer subroutine yields precise approximations for practically any table dimensions and sample size. Key words: contingency tables, independence, chi-square, Kruskal-Wallis, computer algorithm. 1.

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A distributional clustering model for continuous data is reviewed and new methods for optimizing and regularizing it are introduced and compared. Based on samples of discrete-valued auxiliary data associated to samples of the continuous primary data, the continuous data space is partitioned into Voronoi regions that are maximally homogeneous in terms of the discrete data. Then only variation in the primary data associated to variation in the discrete data a#ects the clustering; the discrete data "supervises" the clustering. Because the whole continuous space is partitioned, new samples can be easily clustered by the continuous part of the data alone. In experiments, the approach is shown to produce more homogeneous clusters than alternative methods. Two regularization methods are demonstrated to further improve the results: an entropy-type penalty for unequal cluster sizes, and the inclusion of a model for the marginal density of the primary data. The latter is also interpretable as special kind of joint distribution modeling with tunable emphasis for Preprint submitted to Neurocomputing 23 November 2004 discrimination and the marginal density.

We explain how to apply statistical techniques to solve several language-recognition problems that arise in cryptanalysis and other domains. Language recognition is important in cryptanalysis because, among other applications, an exhaustive key search of any cryptosystem from ciphertext alone requires a test that recognizes valid plaintext. Written for cryptanalysts, this guide should also be helpful to others as an introduction to statistical inference on Markov chains. Modeling language as a finite stationary Markov process, we adapt a statistical model of pattern recognition to language recognition. Within this framework we consider four welldefined language-recognition problems: 1) recognizing a known language, 2) distinguishing a known language from uniform noise, 3) distinguishing unknown 0th-order noise from unknown 1st-order language, and 4) detecting non-uniform unknown language. For the second problem we give a most powerful test based on the Neyman-Pearson Lemma. For the oth...

Abstract. We prove an asymptotic estimate for the number of m ×n non-negative integer matrices (contingency tables) with prescribed row and column sums and, more generally, for the number of integer feasible flows in a network. Similarly, we estimate the volume of the polytope of m × n non-negative real matrices with prescribed row and column sums. Our estimates are solutions of convex optimization problems and hence can be computed efficiently. As a corollary, we show that if row sums R = (r1,..., rm) and column sums C = (c1,..., cn) with r1 +... + rm = c1 +... + cn = N are sufficiently far from constant vectors, then, asymptotically, in the uniform probability space of the m × n non-negative integer matrices with the total sum N of entries, the event consisting of the matrices with row sums R and the event consisting of the matrices with column sums C are positively correlated. 1. Introduction and

A general methodology is presented for finding suitable Poisson log-linear models with applications to multiway contingency tables. Mixtures of multivariate normal distributions are used to model prior opinion when a subset of the regression vector is believed to be nonzero. This prior distribution is studied for two and three-way contingency tables, in which the regression coefficients are interpretable in terms of odds-ratios in the table. Efficient and accurate schemes are proposed for calculating the posterior model probabilities. The methods are illustrated for a large number of two-way simulated tables and for two three-way tables. These methods appear to be useful in selecting the best log-linear model and in estimating parameters of interest that reflect uncertainty in the true model. Key words and phrases: Bayes factors, Laplace method, Gibbs sampling, Model selection, Odds ratios. AMS subject classifications: Primary 62H17, 62F15, 62J12. 1 Introduction 1.1 Bayesian testing...

this paper we adopt the term from [1], and call them CER genes

Clustering by maximizing the dependency between (margin) groupings or partitionings of co-occurring data pairs is studied. We suggest a probabilistic criterion that generalizes discriminative clustering (DC), an extension of the information bottleneck (IB) principle to labeled continuous data. The criterion is the Bayes factor between models assuming dependence and independence of the two cluster sets, and it can be used as a well-founded criterion for IB for small data sets. With suitable prior assumptions the Bayes factor is equivalent to the hypergeometric probability of a contingency table with the optimized clusters at the margins, and for large data it becomes the standard mutual information. An algorithm for two-margin clustering of paired continuous data, associative clustering (AC), is introduced. Genes are clustered to find dependencies between gene expression and transcription factor binding, and dependencies between expression in di#erent organisms.

We present a randomized approximation algorithm for counting contingency tables, m × n non-negative integer matrices with given row sums R = (r1,..., rm) and column sums C = (c1,..., cn). We define smooth margins (R, C) in terms of the typical table and prove that for such margins the algorithm has quasipolynomial N O(ln N) complexity, where N = r1 + · · · + rm = c1 + · · · + cn. Various classes of margins are smooth, e.g., when m = O(n), n = O(m) and the ratios between the largest and the smallest row sums as well as between the largest and the smallest column sums are strictly smaller than the golden ratio (1 + √ 5)/2 ≈ 1.618. The algorithm builds on Monte Carlo integration and sampling algorithms for logconcave densities, the matrix scaling algorithm, the permanent approximation algorithm, and an integral representation for the number of contingency tables.