Exact Goodness-of-Fit Testing for the Ising Model
Name
Uhler_Exact goodness.pdf
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1.14 MB
Format
Adobe PDF
Checksum (MD5)
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Author(s)
Martín del Campo, Abraham
Cepeda, Sarah
Uhler, Caroline
Date Issued
May 2017
Journal
Scandinavian Journal of Statistics
Publisher
Wiley Blackwell
Citation
Martín del Campo, Abraham et al. “Exact Goodness-of-Fit Testing for the Ising Model.” Scandinavian Journal of Statistics 44, 2 (June 2017): 285-306 © 2016 Board of the Foundation of the Scandinavian Journal of Statistics
Version
Original manuscript
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 various test statistics and 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, finding a Markov basis is often computationally intractable. Thus, we develop a Monte Carlo method for exact goodness-of-fit testing for the Ising model that 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.
MIT Department
Massachusetts Institute of Technology. Institute for Data, Systems, and Society
Massachusetts Institute of Technology. Laboratory for Information and Decision Systems
Terms of Use
Creative Commons Attribution-Noncommercial-Share Alike
Persistent DSpace Link
DOI of Published Version
https://doi.org/10.1111/sjos.12251
