Recent advances in Monte Carlo methods allow us to revisit work by de Finetti who suggested the use of approximate exchangeability in the analyses of contingency tables. This paper gives examples of computational implementations using Metropolis Hastings, Langevin, and Hamiltonian Monte Carlo to compute posterior distributions for test statistics relevant for testing independence, reversible or three-way models for discrete exponential families using polynomial priors and Gröbner bases.

中文翻译：

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de Finetti Priors使用Markov链蒙特卡罗计算。

蒙特卡洛方法的最新进展使我们可以重新审视de Finetti的工作，他建议在列联表分析中使用近似可交换性。本文提供了使用Metropolis Hastings，Langevin和Hamiltonian Monte Carlo计算后验分布的示例，这些统计量与多项式先验和Gröbner基相关，用于检验与独立性相关的检验统计量，离散指数族的可逆或三向模型。