Inference for models with implicit likelihood: a statistical review of data-assimilation and model calibration
Seminar Room 2, Newton Institute Gatehouse
AbstractThe development of simulations (eg, computer models) involves what is often referred to as "calibration" and "data assimilation," in face, the inference of parameters or fields related to data through the simulator. In statistics, embedding a simulator in the likelihood relating parameters to data, raises an original challenge due to lack of information about the likelihood. For example, when the simulator is deterministic, its, its derivatives are not known. When the simulator is stochastic, it defines a pdf only available through simulations. This situation is in some sense analogous to the inference of a majority of stochastic differential equations (SDE), where, evne if we can simulate from the model, no likelihood is available.
Many solutions have been proposed to tackle inference problems for computer models and SDE. Mose of them emerged in physics, hydrology, genetics and other areas not directly related to statistics.
Our objective is, first, to group the various ingerence problems in two problems that are well defined in statistics. We will present two examples based on, (i) the reconstruction of past earthquake history and, (ii) palaeoclimate reconstruction using a vegetation model. Second, we review available inference methods, their weaknesses and potential improvements.