|COOKIES: By using this website you agree that we can place Google Analytics Cookies on your device for performance monitoring.|
When Bayesians Can't Handle the Truth
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.
This talk is part of the Statistics series.
This talk is included in these lists:
Note that ex-directory lists are not shown.
Other listsASNC Research Seminar Institute of Astronomy Extra Talks Cambridge Public Policy Seminar Series
Other talksWhat mathematics tell us about the nature of life ... more than 3,800,000,000 years ago! The Conscious Phenotype A Defence of Mathematical Modelling in Economics tba Stem cells and cancer “Nanomedicines for HIV”