Exact goodness-of-fit testing for the Ising model
| Autor: | Caroline Uhler, Sarah Cepeda, Abraham Martín del Campo |
|---|---|
| Přispěvatelé: | Massachusetts Institute of Technology. Institute for Data, Systems, and Society, Massachusetts Institute of Technology. Laboratory for Information and Decision Systems, Uhler, Caroline |
| Jazyk: | angličtina |
| Rok vydání: | 2014 |
| Předmět: |
Statistics and Probability
FOS: Computer and information sciences Monte Carlo method Mathematics - Statistics Theory Statistics Theory (math.ST) 01 natural sciences Methodology (stat.ME) 010104 statistics & probability symbols.namesake Goodness of fit FOS: Mathematics Mathematics - Combinatorics Statistical physics 0101 mathematics Statistics - Methodology Statistical hypothesis testing Mathematics Algebraic statistics Basis (linear algebra) Markov chain 010102 general mathematics Markov chain Monte Carlo symbols Ising model Combinatorics (math.CO) Statistics Probability and Uncertainty 62M02 82B20 78M31 |
| Zdroj: | arXiv |
| Popis: | 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 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. 20 pages |
| Databáze: | OpenAIRE |
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