---
_id: '2016'
abstract:
- lang: eng
  text: 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.
article_processing_charge: No
arxiv: 1
author:
- first_name: Abraham
  full_name: Martin Del Campo Sanchez, Abraham
  last_name: Martin Del Campo Sanchez
- first_name: Sarah A
  full_name: Cepeda Humerez, Sarah A
  id: 3DEE19A4-F248-11E8-B48F-1D18A9856A87
  last_name: Cepeda Humerez
- first_name: Caroline
  full_name: Uhler, Caroline
  id: 49ADD78E-F248-11E8-B48F-1D18A9856A87
  last_name: Uhler
  orcid: 0000-0002-7008-0216
citation:
  ama: Martin Del Campo Sanchez A, Cepeda Humerez SA, Uhler C. Exact goodness-of-fit
    testing for the Ising model. <i>Scandinavian Journal of Statistics</i>. 2017;44(2):285-306.
    doi:<a href="https://doi.org/10.1111/sjos.12251">10.1111/sjos.12251</a>
  apa: Martin Del Campo Sanchez, A., Cepeda Humerez, S. A., &#38; Uhler, C. (2017).
    Exact goodness-of-fit testing for the Ising model. <i>Scandinavian Journal of
    Statistics</i>. Wiley-Blackwell. <a href="https://doi.org/10.1111/sjos.12251">https://doi.org/10.1111/sjos.12251</a>
  chicago: Martin Del Campo Sanchez, Abraham, Sarah A Cepeda Humerez, and Caroline
    Uhler. “Exact Goodness-of-Fit Testing for the Ising Model.” <i>Scandinavian Journal
    of Statistics</i>. Wiley-Blackwell, 2017. <a href="https://doi.org/10.1111/sjos.12251">https://doi.org/10.1111/sjos.12251</a>.
  ieee: A. Martin Del Campo Sanchez, S. A. Cepeda Humerez, and C. Uhler, “Exact goodness-of-fit
    testing for the Ising model,” <i>Scandinavian Journal of Statistics</i>, vol.
    44, no. 2. Wiley-Blackwell, pp. 285–306, 2017.
  ista: 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.
  mla: Martin Del Campo Sanchez, Abraham, et al. “Exact Goodness-of-Fit Testing for
    the Ising Model.” <i>Scandinavian Journal of Statistics</i>, vol. 44, no. 2, Wiley-Blackwell,
    2017, pp. 285–306, doi:<a href="https://doi.org/10.1111/sjos.12251">10.1111/sjos.12251</a>.
  short: A. Martin Del Campo Sanchez, S.A. Cepeda Humerez, C. Uhler, Scandinavian
    Journal of Statistics 44 (2017) 285–306.
date_created: 2018-12-11T11:55:13Z
date_published: 2017-06-01T00:00:00Z
date_updated: 2023-09-19T15:13:27Z
day: '01'
department:
- _id: GaTk
doi: 10.1111/sjos.12251
external_id:
  arxiv:
  - '1410.1242'
  isi:
  - '000400985000001'
intvolume: '        44'
isi: 1
issue: '2'
language:
- iso: eng
main_file_link:
- open_access: '1'
  url: http://arxiv.org/abs/1410.1242
month: '06'
oa: 1
oa_version: Preprint
page: 285 - 306
publication: Scandinavian Journal of Statistics
publication_identifier:
  issn:
  - '03036898'
publication_status: published
publisher: Wiley-Blackwell
publist_id: '5060'
quality_controlled: '1'
related_material:
  record:
  - id: '6473'
    relation: part_of_dissertation
    status: public
scopus_import: '1'
status: public
title: Exact goodness-of-fit testing for the Ising model
type: journal_article
user_id: c635000d-4b10-11ee-a964-aac5a93f6ac1
volume: 44
year: '2017'
...