(This article was originally published at Three-Toed Sloth , and syndicated at StatsBlogs.)

Attention conservation notice: Self-promotion of an academic talk, based on a three-year-old paper, on the arcana of how Bayesian methods work from a frequentist perspective.

Because is snowing relentlessly and the occasional bout of *merely*
freezing air is a blessed relief, I will be escaping to a balmier clime next
week: Cambridgeshire.

- "When Bayesians Can't Handle the Truth", statistics seminar, Cambridge University
*Abstract*: 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 and predictive convergence, and a large deviations principle for the posterior, even in infinite-dimensional hypothesis spaces; and clarify role of the prior and of model averaging as regularization devices. (Paper)*Place and time*: 1 February 2013, 4--5 pm in MR 12, CMS

*Manual trackback*: Brad DeLong

Self-Centered; Bayes, anti-Bayes

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