Σεμινάριο: "Adaptive rates of contraction for spatially inhomogeneous unknowns"
ΚΥΚΛΟΣ ΣΕΜΙΝΑΡΙΩΝ ΣΤΑΤΙΣΤΙΚΗΣ ΜΑΙΟΣ 2022
Ομιλητής: Sergios Agapiou (Department of Mathematics and Statistics, University of Cyprus, CY)
Adaptive rates of contraction for spatially inhomogeneous unknowns
We consider Bayesian approaches to non-parametric models. In particular, we use p-exponential priors, which are priors constructed via random series expansions using distributions with tails between Gaussian and exponential. We will study the frequentist asymptotic performance of the posterior distribution in the infinitely informative data limit, in terms of posterior contraction rates. Priors with exponential rather than Gaussian tails have been shown to be more suitable for modeling spatially inhomogeneous unknown functions, that is functions that are regular in some part and irregular in some other part of their domain.
We will design procedures which give rise to posteriors contracting at rates which are adaptive in the minimax sense, for (Besov) classes of spatially inhomogeneous unknown functions. Specifically, we study p-exponential priors with scaling and regularity hyper-parameters, using empirical Bayes and hierarchical Bayes methods of choosing the hyper-parameters.
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