# Rates of contraction of posterior distributions based on p-exponential priors

Agapiou, Sergios, Dashti, Masoumeh and Helin, Tapio (2021) Rates of contraction of posterior distributions based on p-exponential priors. Bernoulli - Journal of the Bernoulli Society (Bernoulli), 27 (3). pp. 1616-1642. ISSN 1350-7265

However, the specific concentration properties of $p$-exponential priors lead to a more complex entropy bound which can influence negatively the obtained rate of contraction, depending on the topology of the parameter space. Subject to the more complex entropy bound, we show that the rate of contraction depends on the position of the true parameter relative to a certain Banach space associated to $p$-exponential measures and on the small ball probabilities of these measures. For example, we apply our theory in the white noise model under Besov regularity of the truth and obtain minimax rates of contraction using (rescaled) $\alpha$-regular $p$-exponential priors. In particular, our results suggest that when interested in spatially inhomogeneous unknown functions, in terms of posterior contraction, it is preferable to use Laplace rather than Gaussian priors.