Exact goodness-of-fit testing for the Ising model

A. Martin Del Campo Sanchez, S.A. Cepeda Humerez, C. Uhler, Scandinavian Journal of Statistics 44 (2017) 285–306.


Journal Article | Published | English
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; ;
Department
Abstract
The Ising model is one of the simplest and most famous models of interacting systems. It was originally proposed to model ferromagnetic interactions in statistical physics and is now widely used to model spatial processes in many areas such as ecology, sociology, and genetics, usually without testing its goodness-of-fit. Here, we propose an exact goodness-of-fit test for the finite-lattice Ising model. The theory of Markov bases has been developed in algebraic statistics for exact goodness-of-fit testing using a Monte Carlo approach. However, this beautiful theory has fallen short of its promise for applications, because finding a Markov basis is usually computationally intractable. We develop a Monte Carlo method for exact goodness-of-fit testing for the Ising model which avoids computing a Markov basis and also leads to a better connectivity of the Markov chain and hence to a faster convergence. We show how this method can be applied to analyze the spatial organization of receptors on the cell membrane.
Publishing Year
Date Published
2017-06-01
Journal Title
Scandinavian Journal of Statistics
Volume
44
Issue
2
Page
285 - 306
ISSN
IST-REx-ID

Cite this

Martin Del Campo Sanchez A, Cepeda Humerez SA, Uhler C. Exact goodness-of-fit testing for the Ising model. Scandinavian Journal of Statistics. 2017;44(2):285-306. doi:10.1111/sjos.12251
Martin Del Campo Sanchez, A., Cepeda Humerez, S. A., & Uhler, C. (2017). Exact goodness-of-fit testing for the Ising model. Scandinavian Journal of Statistics, 44(2), 285–306. https://doi.org/10.1111/sjos.12251
Martin Del Campo Sanchez, Abraham, Sarah A Cepeda Humerez, and Caroline Uhler. “Exact Goodness-of-Fit Testing for the Ising Model.” Scandinavian Journal of Statistics 44, no. 2 (2017): 285–306. https://doi.org/10.1111/sjos.12251.
A. Martin Del Campo Sanchez, S. A. Cepeda Humerez, and C. Uhler, “Exact goodness-of-fit testing for the Ising model,” Scandinavian Journal of Statistics, vol. 44, no. 2, pp. 285–306, 2017.
Martin Del Campo Sanchez A, Cepeda Humerez SA, Uhler C. 2017. Exact goodness-of-fit testing for the Ising model. Scandinavian Journal of Statistics. 44(2), 285–306.
Martin Del Campo Sanchez, Abraham, et al. “Exact Goodness-of-Fit Testing for the Ising Model.” Scandinavian Journal of Statistics, vol. 44, no. 2, Wiley-Blackwell, 2017, pp. 285–306, doi:10.1111/sjos.12251.

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