改进MCMC方法及其应用

概率反演中，马尔科夫链蒙特卡罗(Markov chain Monte Carlo, MCMC)是一类重要的后验概率进行抽样方法，但由于各种原因MCMC算法搜索往往会陷入局部最优解，从而限制了MCMC方法在具有非唯一解反问题中的应用。鉴于此，提出了一种基于Metropolis-Hastings算法的多链搜索的方法，该方法可以根据搜索结果实时调整链的个数，因而在搜索到尽可能多的解的同时节省了多链搜索的时间。最后将该算法应用于地下水污染源反问题的求解，计算结果表明改进后的算法对求解具有非唯一解反问题具有良好的效果。

Improved MCMC method and its application

In probability inversion, Markov chain Monte Carlo(MCMC) is a kind of methods for sampling posterior probability, but the search based on MCMC algorithm will often get trapped into the local optimal solutions for various reasons, which limits the application of MCMC in solving inverse problems with non-unique solutions. Considering this, a multi-chain sampling method based on Metropolis-Hastings algorithm was developed in this paper, which can adjust the number of chains according to the feedback results from sampling process, so it can search out the non-unique solutions as much as possible while saving the time of multi-chain search. At last, an inverse problem of underground flow was solved using DMMH algorithm. The computational results indicate the improved MCMC algorithm performs well on inverse problems with non-unique solutions.