Reflecting uncertainty in inverse problems: a Bayesian solution using Lévy processes Export

@article{citeulike:4172596, abstract = {We formulate the inverse problem of solving Fredholm integral equations of the first kind as a nonparametric Bayesian inference problem, using Levy random fields (and their mixtures) as prior distributions. Posterior distributions for all features of interest are computed employing novel Markov chain Monte Carlo numerical methods in infinite-dimensional spaces, based on generalizations and extensions of the authors' inverse Levy measure (ILM) algorithm. The method is also well suited for deconvolution problems, for inverting Laplace and Fourier transforms, and for other linear and nonlinear problems in which the unknown feature is high (or even infinite) dimensional and where the corresponding forward problem may be solved rapidly. The methods are illustrated for an application to an important problem in rheology: that of inferring the molecular weight distribution of polymers from conventional rheological measurements, in which we achieve not just a point estimate but a posterior probability density plot representing all uncertainty about the weight.}, author = {Wolpert, Robert L. and Ickstadt, Katja}, citeulike-article-id = {4172596}, citeulike-linkout-0 = {http://dx.doi.org/10.1088/0266-5611/20/6/004}, doi = {10.1088/0266-5611/20/6/004}, journal = {Inverse Problems}, keywords = {bayesian, inverse, problem, rheology}, number = {6}, pages = {1759--1771}, posted-at = {2009-03-13 20:38:18}, priority = {2}, title = {Reflecting uncertainty in inverse problems: a Bayesian solution using L\&\#233;vy processes}, url = {http://dx.doi.org/10.1088/0266-5611/20/6/004}, volume = {20}, year = {2004} }

TY - JOUR ID - citeulike:4172596 L3 - citeulike-article-id:4172596 N2 - We formulate the inverse problem of solving Fredholm integral equations of the first kind as a nonparametric Bayesian inference problem, using Levy random fields (and their mixtures) as prior distributions. Posterior distributions for all features of interest are computed employing novel Markov chain Monte Carlo numerical methods in infinite-dimensional spaces, based on generalizations and extensions of the authors' inverse Levy measure (ILM) algorithm. The method is also well suited for deconvolution problems, for inverting Laplace and Fourier transforms, and for other linear and nonlinear problems in which the unknown feature is high (or even infinite) dimensional and where the corresponding forward problem may be solved rapidly. The methods are illustrated for an application to an important problem in rheology: that of inferring the molecular weight distribution of polymers from conventional rheological measurements, in which we achieve not just a point estimate but a posterior probability density plot representing all uncertainty about the weight. IS - 6 JF - Inverse Problems EP - 1771 TI - Reflecting uncertainty in inverse problems: a Bayesian solution using Lévy processes VL - 20 SP - 1759 KW - bayesian KW - inverse KW - problem KW - rheology AU - Wolpert, Robert AU - Ickstadt, Katja PY - 2004/// UR - http://dx.doi.org/10.1088/0266-5611/20/6/004 ER -