An Efficient Self-Tuning Proposal Distribution for Random Variate Generation With Complex Density Representation

Abstract

Random variate generation has been widely used in various engineering applications and model frameworks. The introduction of the proposal distribution makes this kind of methods can deal with more general sampling problems with complex probability density representation. However, the design of proposal distribution is usually difficult, especially when the target distribution is so complex that it contains asymmetric, multimodal and skewed, or even unsmooth, heavy tailed and illegal density, the sampling performance and efficiency will be greatly affected. In this paper, a novel parameter optimization method with efficient self-tuning strategy is proposed in order to automatically construct the optimal proposal distribution for any complex target density, which treats the design of proposal distribution as a parameter search process and search the optimal solution in an infeasible region by evaluating the loss of solution. The significant advantage of the proposed method is that the search based on infeasible region can converge to a good solution with only a few iterations, making our method far superior to other existing methods in efficiency, which is very suitable for the complex target distribution model with time-consuming density calculation process. Experimental results show the advantages of the proposed method in terms of search strategy, optimal solution performance, search efficiency and robustness.