Quantifying simulator discrepancy in discrete-time dynamical simulators

When making predictions with complex simulators it can be important to quantify the various sources of uncertainty. Errors in the structural specification of the simulator, for example due to missing processes or incorrect mathematical specification, can be a major source of uncertainty, but are often ignored. We introduce a methodology for inferring the discrepancy between the simulator and the system in discrete-time dynamical simulators. We assume a structural form for the discrepancy function, and show how to infer the maximum likelihood parameter estimates using a particle filter embedded within a Monte Carlo expectation maximization (MCEM) algorithm. We illustrate the method on a conceptual rainfall runoff simulator (logSPM) used to model the Abercrombie catchment in Australia. We assess the simulator and discrepancy model on the basis of their predictive performance using proper scoring rules.