Three-Toed Sloth

"When Bayesians Can't Handle the Truth"

Attention conservation notice: Self-promotional; only of interest if you care about theoretical statistics and will be in the Boston area on Monday.

A talk, based on Bayes < Darwin-Wallace paper.

"When Bayesians Can't Handle the Truth"

Harvard Statistics Colloquium

Abstract: When should a frequentist expect Bayesian updating to work? There are elegant results on the consistency of Bayesian updating for well-specified models facing IID or Markovian data, but both completely correct models and fully observed states are vanishingly rare. In this talk, I give conditions for posterior convergence that hold when the prior excludes the truth, which may have complex dependencies. The key dynamical assumption is the convergence of time-averaged log likelihoods (Shannon- McMillan-Breiman property). The main statistical assumption is a building into the prior a form of capacity control related to the method of sieves. With these, I derive posterior convergence and a large deviations principle for the posterior, even in infinite- dimensional hypothesis spaces, extending in some cases to the rates of convergence; and clarify role of the prior and of model averaging as regularization devices. (Paper)

Time and place: 4 pm on Monday, 4 April 2011, Science Center Room 309

Self-centered; Bayes, anti-Bayes