A New Adaptive Rejection Sampling Method Using Kernel Density Approximations and Its Application to Subset Simulation

Abstract

AbstractIn stochastic analysis of engineering systems, the task of generating samples according to a target probability distribution involving some performance function of the system response often arises. This paper introduces an adaptive method for rejection sampling that uses adaptive kernel sampling densities (AKSD) as proposal densities for the rejection sampling algorithm in an iterative approach. The AKSD formulation relies on having available (1) a small number of samples from the target density, as well as (2) evaluations of the system performance function over some other sample set. This information is then used to establish the adaptive features of the stochastic sampling involving (1) an explicit optimization of the kernel characteristics for reduction of the computational burden, and so maximizing sampling efficiency, and (2) selection of the exact model parameters to target so that potential problems when forming proposal densities for high-dimensional vectors are avoided. Beyond this theore...