"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
- Time and place: 4 pm on Monday, 4 April 2011, Science Center Room 309
Posted at April 03, 2011 17:10 | permanent link