Representation of model inputs and parameters using stochastic, time-dependent parameters
Representation of model inputs and parameters using stochastic, time-dependent parameters can improve the accuracy of model predictions and representations of uncertainty. This is because, in deterministic models of environmental systems, systematic discrepancies between model simulations and measured data typically occur. These systematic deviations may be indicative of true indeterminism, or they might be the consequence of model aggregation and simplification. In either case, the implausibility of typical statistical assumptions implies that parameter uncertainty estimates or model extrapolations based on common techniques are likely to be unreliable. To address these discrepancies, we propose making selected parameters in the model time-variable by treating them as continuous-time stochastic processes. We have developed a Markov chain Monte Carlo algorithm for Bayesian estimation of such parameters jointly with the other, constant parameters of the model. The algorithm consists of Gibbs sampling between constant and time-varying parameters using a Metropolis-Hastings algorithm for each parameter type. We have tested our algorithm using a simple global climate model in which an additional stochastic forcing component is introduced. The results show that the algorithm behaves well, is computationally tractable, improves the fit of the model to the data, and provides reasonable estimates of the additional forcing component over most of the simulation period.