Efficient computation for Bayesian comparison of two proportions

Mikkel Nørgaard Schmidt*, Morten Mørup

*Corresponding author for this work

Research output: Contribution to journalJournal articleResearchpeer-review

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In Bayesian comparison of two proportions, the exact computation of the evidence involves evaluating a generalized hypergeometric function. Several agreeing, but not identical, expressions for the evidence have been derived in the literature; however, their practical computation (by summing the truncated hypergeometric series) can be troubled by slow convergence or catastrophic cancellation. Using a set of equivalence relations for the generalized hypergeometric function, we derive ten equivalent expressions for the evidence: We show that one of these formulations, which has not previously been studied, is superior in terms of its computational properties. We recommend that this be used instead of existing formulations, and provide an efficient software implementation.

Original languageEnglish
JournalStatistics and Probability Letters
Pages (from-to)57-62
Publication statusPublished - 2018


  • Bayesian analysis
  • Comparison of proportions
  • Integral of beta distribution
  • Hypergeometric function


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