Algebraic exact inference for rater agreement models |
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Authors: | Fabio Rapallo |
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Institution: | (1) Department of Mathematics, University of Genova, via Dodecaneso 35, 16146 Genova, Italy |
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Abstract: | In 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.
Partially supported by MIUR Cofin03 (G. Consonni) and by INdAM projectAlgebraic Statistics. |
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Keywords: | Cohen's kappa Conditional inference Diaconis-Sturmfels algorithm Log-linear models |
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