LOCAL ADAPTIVE IMPORTANCE SAMPLING FOR MULTIVARIATE DENSITIES WITH STRONG NONLINEAR RELATIONSHIPS

We consider adaptive importance sampling techniques that use kernel de nsity estimates at each iteration as importance sampling functions. Th ese can provide more nearly constant importance weights and more preci se estimates of quantities of interest than the sampling importance re sampling algorithm when the initial importance sampling function is di ffuse relative to the target. We propose a new method that adapts to t he varying local structure of the target. When the target has unusual structure, such as strong nonlinear relationships between variables, t his method provides estimates with smaller mean squared error than alt ernative methods.