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Center for Nonlinear Studies |
A well-known weakness of (ensemble) Monte Carlo is its slow rate of convergence. In general the rate of convergence cannot be improved upon, hence, since the inception of the MC method, a number of variance reduction (VR) techniques have been devised to reduce the variance of the MC estimator. All VR techniques bring some additional/external information to bear on the estimation problem and rely on the existence of specific problem features and the ability of the user of the method to discover and effectively exploit such features. This lack of generality has significantly limited the applicability of VR techniques. We present a new strategy, called DataBase Monte Carlo (DBMC), which aims to address this shortcoming by divising generic VR techniques that can be generically applied. The core idea of the approach is to extract information at one or more nominal model parameters and use this information to gain estimation efficiency at neighboring parameters. We describe how this strategy can be implemented using two variance reduction techniques: Control Variates (CV) and Stratification (DBMC approach can be used more broadly and is not limited to these two techniques). We show that, once an initial setup cost of generating a database is incurred, this approach can lead to dramatic gains in computational efficiency. DBMC is quite general and easy to implement -- it can wrap existing ensemble MC codes. As such it has potential applications, among others, in ensemble weather prediction, hydrological source location, climate and ocean, optimal control, and stochastic simulations of biological systems. We discuss connections of the DBMC approach with the resampling technique of Bootstrap and the analysis approach of Information Based Complexity.
Host: Frank Alexander, ADTSC