Data Integration using the Probability Perturbation Method

Abstract

A new method, termed probability perturbation, is developed for solving non-linear inverse problem under a prior model constraint. The method proposed takes a different route from the traditional Bayesian inverse models that rely on prior and likelihood distribution for stating, then sampling, from a posterior distribution. Instead, the probability perturbation method relies on so-called pre-posterior distributions, which state the distribution of the unknown parameter set given each individual data type (linear or non-linear). Sampling consists of perturbing the probability models used to generate the model realization, by which a chain of realizations is created that converge to match any type of data. The probability perturbations are such that the underlying spatial structure (prior model) of the stochastic algorithm is maintained through all perturbations. A simple example illustrates the approach.