Use of sequential structure in simulation from high-dimensional systems

Sampling from high-dimensional systems often suffers from the curse of dimensionality. In this paper, we explored the use of sequential structures in sampling from high-dimensional systems with an aim at eliminating the curse of dimensionality, and proposed an algorithm, so-called sequential parallel tempering as an extension of parallel tempering. The algorithm was tested with the witch's hat distribution and Ising model. Numerical results suggest that it is a promising tool for sampling from high-dimensional systems. The efficiency of the algorithm was argued theoretically based on the Rao-Blackwellization theorem.