Local Adaptive Importance Sampling for Multivariate Densities with Strong Nonlinear Relationships

We consider adaptive importance sampling techniques which use kernel density estimates at each iteration as importance sampling functions. These can provide more nearly constant importance weights and more precise estimates of quantities of interest than the SIR algorithm when the initial importance sampling function is di use relative to the target. We propose a new method which adapts to the varying local structure of the target. When the target has unusual structure, such as strong nonlinear relationships between variables, this method provides estimates with smaller MSE than alternative methods.