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The semiparametric Bernstein-Von Mises theorem

Kleijn, B (Free University)
Thursday 27 March 2008, 11:00-12:00

Seminar Room 2, Newton Institute Gatehouse


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.)


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