de Finetti Priors using Markov chain Monte Carlo computations

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.