Title: Rates of posterior contraction for spatially inhomogeneous unknowns
Authors: Sergios Agapiou - University of Cyprus (Cyprus) [presenting]
Masoumeh Dashti - University of Sussex (United Kingdom)
Tapio Helin - LUT University (Finland)
Abstract: Some recent results on frequentist convergence rates of the posterior distribution in nonparametric settings will be discussed. In particular, we will consider a class of prior distributions, with tails between Gaussian and exponential, called p-exponential priors. This class includes the 1-Besov priors, which are especially popular in the applied Bayesian inverse problems community due to their sparsity promoting and edge-preserving properties. We will present a general theory, and then we will focus on the white noise model with alpha-regular p-exponential priors. We will discuss contraction rates over Besov regularity of the truth which suggest that when interested in spatially inhomogeneous unknown functions, in terms of posterior contraction, it is preferable to use Laplace rather than Gaussian priors.