Sampling Normal Distribution Restricted on Multiple Regions

We develop an accept-reject sampler for probability densities that have the similar form of a normal density function, but supported on restricted regions. Compared to existing techniques, the proposed method deals with multiple disjoint regions, truncated on one or both sides. For the original problem of sampling from one region, the efficiency is enhanced as well. We verify the desirable attributes of the proposed algorithm by both theoretical analysis and simulation studies.