Posterior Convergence Analysis of α-Stable Sheets

07/06/2019
by   Neil K. Chada, et al.
0

This paper is concerned with the theoretical understanding of α-stable sheets U on R^d. Our motivation for this is in the context of Bayesian inverse problems, where we consider these processes as prior distributions, aiming to quantify information of the posterior. We derive convergence results referring to finite-dimensional approximations of infinite-dimensional random variables. In doing so we use a number of variants which these sheets can take, such as a stochastic integral representation, but also random series expansions through Poisson processes. Our proofs will rely on the fact of whether U can omit L^p-sample paths. To aid with the convergence of the finite approximations we provide a natural discretization to represent the prior. Aside from convergence of these stable sheets we address whether both well-posedness and well-definiteness of the inverse problem can be attained.

READ FULL TEXT

page 1

page 2

page 3

page 4

07/06/2019

Posterior Convergence of α-Stable Sheets

This paper is concerned with the theoretical understanding of α-stable s...
10/16/2017

Well-posedness of Bayesian inverse problems in quasi-Banach spaces with stable priors

The Bayesian perspective on inverse problems has attracted much mathemat...
12/18/2015

Expectation propagation for continuous time stochastic processes

We consider the inverse problem of reconstructing the posterior measure ...
12/08/2017

Posterior distribution existence and error control in Banach spaces

We generalize the results of Christen2017 on expected Bayes factors (BF)...
10/29/2019

ε-strong simulation of the convex minorants of stable processes and meanders

Using marked Dirichlet processes we characterise the law of the convex m...
02/28/2021

Random tree Besov priors – Towards fractal imaging

We propose alternatives to Bayesian a priori distributions that are freq...
09/14/2018

Canonical spectral representation for exchangeable max-stable sequences

The set of infinite-dimensional, symmetric stable tail dependence functi...