A connection between Bayesian and frequentist estimates

Shande Chen

Research output: Contribution to journalArticlepeer-review


For finite sample size, the traditional Bayes estimator depends on the choice of the prior. On the other hand, a frequentist estimator, such as MLE does not use any prior for the parameter(s). In general, a Bayes estimator and a frequentist estimator could be quite different when the sample size is not large. In this article, we provide results showing that the MLE can be obtained as a limiting Bayes estimator by keeping updating the prior. The convergence is independent of the choice of the prior. Some examples using conjugate priors are also provided.

Original languageEnglish
Pages (from-to)15-19
Number of pages5
JournalJournal of Applied Probability and Statistics
Issue number1
StatePublished - 1 Jan 2015


  • Conjugate prior
  • Convergence to a point mass
  • Empirical Bayes
  • Maximum likelihood estimator


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