Research On Application Of Several Variance Reduction Techniques

The Monte Carlo(MC)method as a statistical method was initially used primarily to supplement the deterministic method.The popularity and application of computers breaking the situation with the rapid development of computers,the original simulation process that is time-consuming has become more efficient,this chance greatly contributed to the development of MC methods.The range of application of the MC method from the beginning of the nuclear field also extended to other areas.Now the MC method has solved many problems in the field of physics,engineering,finance and other important computing tools,the investment risk in the parameter estimation and reliability design and bid quotation biomedical statistical physics and MC method has the extremely widespread application.The certainty problems also can use the MC method and all kinds of equations(group)and calculate multiple integral,infinite series,etc.However,since the approximation of MC method with random simulation is inevitably to deviate the estimated true value,following this problem we study in this paper.Firstly,the convergence of the MC method and error estimates have been analyzed in this paper,and six kinds of variance reduction methods which were commonly used have been summarized.Six kinds of variance have been presented,such as important sampling method,the control variable method,antithetic variables method,conditioning expectation method,stratified sampling method,related sampling method.Secondly,in this paper,MC antithetic variables method is discussed with system of equations,definite integral and series.Estimated values based on related sampling method can be achieved by constructing probability and statistics models and sampling for random samples.The result shows that this technique can reduce the simulation precision and shorten the computer running time effectively.Finally,we discuss the adaptive Monte Carlo solution algorithm of linear algebraic system.The adaptive Monte Carlo method includes adaptive importance sampling Monte Carlo and adaptive correlation sampling Monte Carlo,comparing Monte Carlo method anddeterministic method by solving concrete examples,the efficiency of the algorithm is obtained,and the adaptive Monte Carlo method can obtain a faster convergence rate.