An Improved Markov Chain Monte Carlo Scheme for Parameter Estimation Analysis

Aiming at resolving the issue of designing appropriate proposal distribution in Markov Chain Monte Carlo (MCMC) algorithm, an improved MCMC scheme is developed in this paper. The presented scheme employs normal density distribution as proposal distribution to sample in objective function, and together with the historical sampling information, the proposal distribution runs to proper distribution by adaptive self-regulation. The improved scheme is applied to parameter estimation of Pearson-III distribution to figure out the problems of runoff frequency forecast. In the case study of annual runoff frequency calculation of Fengtan reservoir, satisfying results are obtained, and compared with the genetic algorithm and the traditional weight function method, the new scheme can not only provide the proper posterior distribution, but also the related statistical information of parameters, which are useful for parameter estimation of complex modeling and uncertainty analysis.