High-dimensional simulation-based estimation

This paper describes a simulation-based technique for estimating the parame ters of a high-dimensional stochastic model. The central idea is to find pa rameters which make the distribution of simulated multidimensional points Y identical to the distribution of the multidimensional points X observed in experiments. To do this, we minimize a criterion based on the heuristic th at the univariate distribution of distances between the Ys and the Xs shoul d be the same as the univariate distribution of distances among the replica ted Xs themselves. The direction of random local searches in the parameter space for the minimizing value are guided by (i) the degree of success of recent searches, and (ii) a multiple regression fit of the recently investigated portion of the criterion's response surface to a deterministic approximation of the stocha stic model which can be rapidly investigated. This approximation is most likely to be used when it is most valid, that is when R-2 is close to one. To guard against entrapment at a local minimum, the algorithm at random times will search the global parameter space to loo k for promising other portions to investigate. Unlike simulated annealing, where the criterion function can be evaluated exactly, our algorithm must d eal with the fact that the observed value of the criterion for a given set of parameters is itself based on simulation and thus subject to variability . This difficulty is handled through a cross-validation procedure which exa mines the distribution of the criterion at the last successful point. The m ethodology is applied to a detailed stochastic predator-prey model original ly described in [1]. (C) 2000 Elsevier Science Ltd. All rights reserved.