On the validity of the formal edgeworth expansion for posterior densities

John E. Kolassa, Todd A. Kuffner

Research output: Contribution to journalArticlepeer-review

4 Scopus citations


We consider a fundamental open problem in parametric Bayesian theory, namely the validity of the formal Edgeworth expansion of the posterior density. While the study of valid asymptotic expansions for posterior distributions constitutes a rich literature, the validity of the formal Edgeworth expansion has not been rigorously established. Several authors have claimed connections of various posterior expansions with the classical Edgeworth expansion, or have simply assumed its validity. Our main result settles this open problem. We also prove a lemma concerning the order of posterior cumulants which is of independent interest in Bayesian parametric theory. The most relevant literature is synthesized and compared to the newly-derived Edgeworth expansions. Numerical investigations illustrate that our expansion has the behavior expected of an Edgeworth expansion, and that it has better performance than the other existing expansion which was previously claimed to be of Edgeworth type.

Original languageEnglish (US)
Pages (from-to)1940-1958
Number of pages19
JournalAnnals of Statistics
Issue number4
StatePublished - Aug 2020

All Science Journal Classification (ASJC) codes

  • Statistics and Probability
  • Statistics, Probability and Uncertainty


  • Cumulant expansion
  • Edgeworth expansion
  • Higher-order asymptotics
  • Posterior


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