James Martin

TL;DR: This work addresses the solution of large-scale statistical inverse problems in the framework of Bayesian inference with a so-called Stochastic Monte Carlo method.

TL;DR: In this article, the uncertainty in the numerical solution of linearized infinite-dimensional statistical inverse problems is estimated using the Bayesian inference formulation, where the prior probability distribution is chosen appropriately in order to guarantee wellposedness of the inverse problem and facilitate computation of the posterior.

TL;DR: Bui-Thanh et al. as mentioned in this paper considered the numerical solution of infinite-dimensional inverse problems in the framework of Bayesian inference and used a Markov chain Monte Carlo (MCMC) sampling method.

TL;DR: In this paper, a low-rank update of the prior covariance matrix is proposed to characterize and approximate the posterior distribution of the parameters in inverse problems, based on the leading eigendirections of the matrix pencil defined by the Hessian of the negative log-likelihood and the prior precision.

TL;DR: In this paper, a likelihood-informed subspace (LIS) is defined and identified by characterizing the relative influences of the prior and the likelihood over the support of the posterior distribution, which enables more efficient computational methods for Bayesian inference with nonlinear forward models and Gaussian priors.