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The semiparametric Bernstein-Von Mises theorem

Presented by: 
B Kleijn [Free University]
Thursday 27th March 2008 - 11:00 to 12:00
INI Seminar Room 2

The Bernstein-Von Mises theorem provides a detailed relation between frequentist and Bayesian statistical methods in smooth, parametric models. It states that the posterior distribution converges to a normal distibution centred on the maximum-likelihood estimator with covariance proportional to the Fisher information. In this talk we consider conditions under which such an assertion holds for the marginal posterior of a parameter of interest in semiparametric models. From a practical point of view, this enables the use of Bayesian computational techniques (e.g. MCMC simulation) to obtain (hard to compute otherwise) frequentist confidence intervals. (Joint work with P. Bickel.)

Presentation Material: 
University of Cambridge Research Councils UK
    Clay Mathematics Institute London Mathematical Society NM Rothschild and Sons