Statistics and Computing

, Volume 25, Issue 4, pp 797–808 | Cite as

de Finetti Priors using Markov chain Monte Carlo computations

  • Sergio Bacallado
  • Persi Diaconis
  • Susan HolmesEmail author


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.


Priors MCMC Contingency tables  Bayesian inference Independence 

Mathematics Subject Classification

62C10 62C25 



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.

Supplementary material

11222_2015_9562_MOESM1_ESM.pdf (573 kb)
Supplementary material 1 (pdf 572 KB)


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Copyright information

© Springer Science+Business Media New York 2015

Authors and Affiliations

  • Sergio Bacallado
    • 1
  • Persi Diaconis
    • 1
  • Susan Holmes
    • 1
    Email author
  1. 1.Sequoia HallStanford UniversityStanfordUSA

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