Kim Emil Andersen

Bayesian inversion of geoelectrical resistivity data

Enormous quantities of geoelectrical data are produced daily and often used for large scale reservoir modelling. To interpret these data requires reliable and efficient inversion methods which adequately incorporate prior information and use realistically complex modelling structures. We use models based on random coloured polygonal graphs as a powerful and flexible modelling framework for the layered composition of the Earth and we contrast our approach with earlier methods based on smooth Gaussian fields. We demonstrate how the reconstruction algorithm may be efficiently implemented through the use of multigrid Metropolis-coupled Markov chain Monte Carlo methods and illustrate the method on a set of field data. Copyright 2003 Royal Statistical Society.

A Bayesian approach to crack detection in electrically conducting media

In this paper, we review powerful new computational techniques which facilitate the Bayesian approach to statistical inference and discuss how they may be used to solve general inverse problems. Their power and flexibility is illustrated by the problem of detecting a finite set of linear non-intersecting perfectly insulating cracks in a homogeneously electrically conducting medium. In this case, efficient algorithms only exist if the number of cracks is known a priori. However, in this paper we demonstrate how uncertainty about the number of cracks can be incorporated into the modelling process and assessed together with crack locations.

Multiplicative censoring: density estimation by a series expansion approach

Abstract We consider the linear inverse problem of recovering the density function for a sample of multiplicatively censored random variables. This is a problem arising in, e.g. estimation of waiting time distributions of renewal processes. The purpose of this paper is to present an approach to this problem using a singular value decomposition of the desired density. We establish conditions under which the rate of convergence of the mean integrated square error of the estimator is optimal. An empirical method for determining the order of expansion is suggested. Finite sample properties of the estimation procedure are studied on a simulated data example.