AMS2008-3: Fast Bayesian Inference for Computer Simulation Inverse Problems

Matthew Taddy, Herbert K. H. Lee, and Bruno Sansó
01/03/2008 09:00 AM
Applied Mathematics & Statistics
Computer models that simulate phenomena regulated by complicated dependencies on unknown parameters are increasingly used in environmental applications. In this paper we present two such applications where the values of the parameters need to be inferred from scarce observations and abundant simulated output. One consists of a climate simulator and the other of a groundwater flow model. Detailed exploration of the parameter space for a computer simulator can be costly, as running the code for a given parameter configuration can be very time consuming. The common Bayesian approach is to develop a surrogate model for the simulator and to use it to find the likelihood for sampling from the posterior distribution of inputs without having to re-run the simulator. However, in many cases like the ones presented in this paper, there is a large bank of simulated values and the need for a faster algorithm that does not require predicted output at new locations. We discuss a sampling importance resampling (SIR) algorithm that works in conjunction with kernel density estimation to resample from the original computer output according to the posterior distribution of input values, which allows for a fully Bayesian analysis without the need for MCMC.