title: Bayesian inference in the scaling analysis of critical phenomena.
abstract: To determine the universality class of critical phenomena, we propose a method of statistical inference in the scaling analysis of critical phenomena. The method is based on Bayesian statistics, most specifically, the Gaussian process regression. It assumes only the smoothness of a scaling function, and it does not need a form. We demonstrate this method for the finite-size scaling analysis of the Ising models on square and triangular lattices. Near the critical point, the method is comparable in accuracy to the least-square method. In addition, it works well for data to which we cannot apply the least-square method with a polynomial of low degree. By comparing the data on triangular lattices with the scaling function inferred from the data on square lattices, we confirm the universality of the finite-size scaling function of the two-dimensional Ising model.
authors.affiliation: Graduate School of Informatics, Kyoto University, Kyoto, Japan.
authors.forename: Kenji
authors.initials: K
authors.lastname: Harada
mesh_terms: D000465:Algorithms; D001499:Bayes Theorem; D016011:Normal Distribution; D010825:Physics / Q000379:methods*; D012044:Regression Analysis; D015203:Reproducibility of Results