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de Finetti Priors using Markov chain Monte Carlo computations

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Abstract

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.

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Acknowledgments

We thank Ben Callahan for discussions about the DNA denoising example. This work was partially funded by Grant NSF-DMS-1162538 to SH, Grant NSF-DMS-1208775 to PD and a CIMI fellowship that funded the travel of all three authors to Toulouse in 2014.

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Correspondence to Susan Holmes.

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Bacallado, S., Diaconis, P. & Holmes, S. de Finetti Priors using Markov chain Monte Carlo computations. Stat Comput 25, 797–808 (2015). https://doi.org/10.1007/s11222-015-9562-9

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Keywords

  • Priors
  • MCMC
  • Contingency tables
  • Bayesian inference
  • Independence

Mathematics Subject Classification

  • 62C10
  • 62C25