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de Finetti Priors using Markov chain Monte Carlo computations.

Sergio Bacallado1, Persi Diaconis1, Susan Holmes1

  • 1Sequoia Hall, Stanford University.

Statistics and Computing
|September 29, 2015
PubMed
Summary

This study revisits de Finetti

Area of Science:

  • Statistics
  • Computational Statistics
  • Bayesian Inference

Background:

  • De Finetti's concept of approximate exchangeability offers a framework for analyzing contingency tables.
  • Traditional methods may not fully leverage modern computational techniques for these analyses.

Purpose of the Study:

  • To explore the application of advanced Monte Carlo methods to de Finetti's approximate exchangeability for contingency tables.
  • To demonstrate computational implementations for testing independence and various models in discrete exponential families.

Main Methods:

  • Utilizing Metropolis Hastings, Langevin, and Hamiltonian Monte Carlo algorithms.
  • Computing posterior distributions for relevant test statistics.
  • Employing polynomial priors and Gröbner bases for discrete exponential families.
Keywords:
Bayesian InferenceContingency TablesIndependenceMCMCPriors

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Main Results:

  • Demonstration of computational feasibility for applying approximate exchangeability.
  • Posterior distributions computed for test statistics under different models.
  • Successful integration of advanced Monte Carlo methods with polynomial priors and Gröbner bases.

Conclusions:

  • Advanced Monte Carlo methods provide a viable computational approach for approximate exchangeability in contingency table analysis.
  • The implemented methods are suitable for testing independence and complex models within discrete exponential families.