Bayesian Linear Inverse Problems in Regularity Scales with Discrete Observations

We obtain rates of contraction of posterior distributions in inverse problems with discrete observations. In a general setting of smoothness scales we derive abstract results for general priors, with contraction rates determined by discrete Galerkin approximation. The rate depends on the amount of prior concentration near the true function...

Decompounding discrete distributions: A nonparametric Bayesian approach

Suppose that a compound Poisson process is observed discretely in time and assume that its jump distribution is supported on the set of natural numbers. In this paper we propose a nonparametric Bayesian approach to estimate the intensity of the underlying Poisson process and the distribution of the jumps. We provide a Markov chain Monte Carlo...

A non-parametric Bayesian approach to decompounding from high frequency data

Given a sample from a discretely observed compound Poisson process, we consider non-parametric estimation of the density f0 of its jump sizes, as well as of its intensity λ0. We take a Bayesian approach to the problem and specify the prior on f0 as the Dirichlet location mixture of normal densities. An independent prior for λ0 is assumed to be...