--- _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 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. Scandinavian Journal of Statistics. 2017;44(2):285-306. doi:10.1111/sjos.12251 apa: 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. Wiley-Blackwell. https://doi.org/10.1111/sjos.12251 chicago: 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. Wiley-Blackwell, 2017. https://doi.org/10.1111/sjos.12251. ieee: 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. 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.” Scandinavian Journal of Statistics, vol. 44, no. 2, Wiley-Blackwell, 2017, pp. 285–306, doi:10.1111/sjos.12251. 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' ...