Slice Sampler For Parallel Tempering And Its Applications

Adding auxiliary variables is an important idea of the development of MCMC method,which increasing the dimension of state space can make sampling move more freely,overcome the “local trap" effectively,and improve its efficiency.Under the influence of this idea,many special MCMC sampling algorithms have been produced in different situations,such as slice sampler and parallel tempering.Under certain conditions,they have a lot of advantages,but there are still some limitations: the former needs to produce uniformly distributed samples in some complex regions,which is difficult to sample accurately;the latter requires sufficient overlap between adjacent temperature distributions,which highly depend on some parameters.In view of the above discussion,firstly,this paper clarify the relationship between slice sampler and parallel tempering algorithm and their advantages in application under the thought of auxiliary variables.Then,a new method,named “discrete slice sampling algorithm”,is proposed to implement the “slice transferring” effectively on single chain.Combining the advantages of parallel tempering,an improved version is presented for parallel chains,named "slice tempering sampler,which can improve the sampling efficiency and reduce the excessive dependence on temperature parameters.After that,the convergence of the slice tempering sampler is proved,and its simulation results show that the algorithm has some advantages over the traditional MCMC methods in the efficiency of mixing and parameter estimation.Finally,the new algorithm is applied to estimate the parameters of the mixture model and a Bayesian analysis of the consumer price index.The relevant results show that the method is effective.