1,721,000 research outputs found
A class of statistical models to weaken independence in two-way contingency tables
No full textAlgebraic Statistics, Log-linear models, Markov bases, Sufficient statistic,
Probability matrices, non-negative rank, and parameterization of mixture models
No full textAbstractIn this paper, we parameterize non-negative matrices of sum one and rank at most two using the least possible number of parameters. We also show how this parameterization relates to a class of statistical models, known in Probability and Statistics as mixture models for contingency tables. In particular, we show how to use this parameterization to make some optimization problems computationally easier
Analysis of the Weighted Kappa and Its Maximum with Markov Moves
No full textIn this paper, the notion of Markov move from algebraic statistics is used to analyze the weighted kappa indices in rater agreement problems. In particular, the problem of the maximum kappa and its dependence on the choice of the weighting schemes are discussed. The Markov moves are also used in a simulated annealing algorithm to actually find the configuration of maximum agreement
Exact inference and conditioning structures for Cohen's kappa with algebraic algorithms
No full textIn questo lavoro presentiamo un algoritmo per l'inferenza esatta sull'indice kappa di Cohen nel caso multivariato. Tale algoritmo è basato su tecniche di Algebra Commutativa che permettono di campionare efficientemente dallo spazio delle tabelle di contingenza multidimensionali con margini fissati. Forniamo inoltre alcune osservazioni sulla struttura del condizionamento e sull'uso delle differenti versioni dell'indice kappa utili in molte applicazioni a problemi di rater agreement multivariato
Outliers and patterns of outliers in contingency tables with algebraic statistics
No full textIn this paper, we provide a definition of pattern of outliers in contingency tables within a model-based framework. In particular, we make use of log-linear models and exact goodness-of-fit tests to specify the notions of outlier and pattern of outliers. The language and some techniques from Algebraic Statistics are essential tools to make the definition clear and easily applicable. We also analyse several numerical examples to show how to use our definitions
Algebraic exact inference for rater agreement models
No full textIn recent years, a method for sampling from conditional distributions for categorical data has been presented by Diaconis and Sturmfels. Their algorithm is based on the algebraic theory of toric ideals which are used to create so called "Markov Bases". The Diaconis-Sturmfels algorithm leads to a non-asymptotic Monte Carlo Markov Chain algorithm for exact inference on some classes of models, such as log-linear models. In this paper we apply the Diaconis-Sturmfels algorithm to a set of models arising from the rater agreement problem with special attention to the multi-rater case. The relevant Markov bases are explicitly computed and some results for simplify the computation are presented. An extended example on a real data set shows the wide applicability of this methodology
Exact conditional inference on h-sample problems for categorical data using algebraic algorithms
No full textAlgebraic Markov Bases and MCMC for Two-Way Contingency Tables
No full textThe Diaconis-Sturmfels algorithm is a method for sampling from conditional distributions, based on the algebraic theory of toric ideals. This algorithm is applied to categorical data analysis through the notion of Markov basis. An application of this algorithm is a non-parametric Monte Carlo approach to the goodness of fit tests for contingency tables. In this paper, we characterize or compute the Markov bases for some log-linear models for two-way contingency tables using techniques from Computational Commutative Algebra, namely Gröbner bases. This applies to a large set of cases including independence, quasi-independence, symmetry, quasi-symmetry. Three examples of quasi-symmetry and quasi-independence from Fingleton ("Models of category counts", Cambridge University Press, Cambridge, 1984) and Agresti ("An Introduction to categorical data analysis", Wiley, New York, 1996) illustrate the practical applicability and the relevance of this algebraic methodology. Copyright 2003 Board of the Foundation of the Scandinavian Journal of Statistics..
The geometry of statistical models for two-way contingency tables with fixed odds ratios
Full text linkWe study the geometric structure of the statistical models for two-by-two contingency tables. One or two odds ratios are fixed and the corresponding models are shown to be a portion of a ruled quadratic surface or a segment. Some pointers to the general case of two-way contingency tables are also given and an application to case-control studies is presented
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