The next statistics seminar will take place tomorrow,
Friday 1 November at 3:10pm, room JCMB5323.
Speaker: Natalia Bochkina (University of Edinburgh)
Title: "Bayesian inference for non-regular models"
Abstract:
We study the asymptotic behaviour of the posterior distribution in a
broad class of statistical models where the ``true'' solution occurs
on the boundary of the parameter space. We show that in this case the
Bayesian inference is consistent, and that the posterior distribution
has not only Gaussian components as in the case of regular models (the
Bernstein--von Mises theorem) but also has Gamma distribution components
that depend on the behaviour of the prior distribution on the boundary
and have a faster rate of convergence. We also show a remarkable
property of Bayesian inference that for some models, the unknown
parameter can be estimated with arbitrarily high precision, if this
parameter is on the boundary of the parameter space, that is, there is
no positive lower bound on the variance of such asymptotically unbiased
estimator, as is the case for regular models.
The results are illustrated on a problem from emission tomography. This
work is joint with Peter Green, University of Bristol.
This seminar is joint with BioSS, and it is a part of Maxwell institute
seminar series.
Website: http://www.maths.ed.ac.uk/events/statistics
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