When Bayesians Can't Handle the Truth

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• Cosma Shalizi, Carnegie Mellon University
• Friday 01 February 2013, 16:00-17:00
• MR12, CMS, Wilberforce Road, Cambridge, CB3 0WB.

If you have a question about this talk, please contact Richard Samworth.

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: http://projecteuclid.org/euclid.ejs/1256822130

This talk is part of the Statistics series.

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