The Bayesian approximation error (BAE) approach belongs to the class of approximate Bayesian computation, with specific focus on inverse problems. The target is to carry out severe model reduction, to use approximate (physical) models and to neglect the estimation of various uninteresting (distributed) parameters. Inverse problems, by definition, do not tolerate the related errors (without feasible modelling of these). The key is to propagate the related errors to an additive error term and then formally marginalize over this vector-valued random variable. At this stage, a normal approximation for the likelihood distribution is usually adopted and point and spread (covariance) estimates are computed.<\/p>\n\n\n\n
The approach has proven to work with different types of modelling errors and approximations such as severe model reduction, unknown boundary data (or operators), approximate physical models, marginalization over uninteresting distributed parameters, domain geometry and truncated decompositions of unknowns.<\/p>\n\n\n\n