Robert Gaunt - Normal approximation for the posterior in exponential families (in-person)
| Dates: | 23 November 2022 |
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| Times: | 15:00 - 16:00 |
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| What is it: | Seminar |
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| Organiser: | Department of Mathematics |
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Robert Gaunt (University of Manchester) will speak in the Probability seminar. (in-person)
The Bernstein-von Mises (BvM) Theorem is a cornerstone in Bayesian statistics. Loosely put, this theorem reconciles Bayesian and frequentist large sample theory by guaranteeing that, under regularity conditions, suitable scalings of posterior distributions are asymptotically normal. In particular, this implies that the contribution of the prior vanishes in the asymptotic posterior.
In this talk, we demonstrate how the probabilistic technique Stein's method can be used to derive explicit optimal order total variation and Wasserstein distance bounds to quantify this distributional approximation for posterior distributions in exponential family models. We apply our general bounds to some classical conjugate prior models and observe that the resulting bounds have an explicit dependence on the prior distribution and on sufficient statistics of the data from the sample, and thus provide insight into how these factors may affect the quality of the normal approximation.
This is joint work with Adrian Fischer, Gesine Reinert and Yvik Swan.
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Frank Adams Room 2
Alan Turing Building
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