The Leading Edge · 1992 · 44 citations · 0 references
ComputingComputer ScienceAlgorithmsStatistical ModelingUncertainty QuantificationBayesian InferenceBayesian ModelingBayesian StatisticsGenetic AlgorithmsInverse ProblemsStatistical InferenceBayesian Inverse ProblemsBayesian InversionComputational Inverse ProblemsGlobal Search AlgorithmsInverse Problem TheoryOptimization-based InversionPosterior Model ProbabilitiesPosterior Probability Assessment
Inverse problems can be formulated as Bayesian inference, combining prior plausibility, data and error information, and numerical/theoretical uncertainties into a posterior probability over all models. The study aims to identify all models whose posterior probability exceeds a user‑specified acceptability threshold. Optimization procedures are employed to extremize the posterior probability function, thereby locating the models that meet the threshold.
A very general and flexible way to formulate inverse problems is as problems in Bayesian inference. This approach permits us to consolidate a number of different types of information about a particular inverse problem into a single calculation. We can combine a priori information about which model features are plausible and which are not, information about the observed data and their errors, and information about numerical and theoretical errors in the calculation that predicts the data that would be produced by a given model. We end up with a scalar‐valued function, called the posterior probability, over the space of all models. The values of this function over a set of models express the probability that those models could have led to a particular set of observed data. The goal of the inverse calculation, then, is to find all of the models whose posterior probability is greater than some threshold of acceptability set in advance by the user. (The function that optimization calculations seek to extremize...