Global search and genetic algorithms

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 is often called the objective function; the posterior probability is used as an objective function when we try to solve inference problems.)