The HMC Sampling Method Applied In Approximate Bayesian Computation With Synthetic Likelihood And Application

In recent years,Approximate Bayesian Computation is a kind of popular Bayesian computation method with free likelihood,mainly used in complex models to solve the parameter estimation problem when the likelihood function is difficult to be expressed analytically.In this paper,Bayesian computation with empirical likelihood(BCel)and Bayesian computation with synthetic likelihood(BCsl)were used to conduct numerical simulation experiments on SV-N model and SV-T model respectively.In terms of accuracy of parameter estimation and program operation efficiency,BCel algorithm was more suitable for parameter estimation of SV model.After that,this paper takes Shanghai composite index as the research object,according to the characteristics of the daily return rate of Shanghai composite index,such as leptokurtosis and fat-tail and volatility-clustering,etc.,this paper chooses the optimal algorithm BCel algorithm to estimate parameters of SV-T model,and analyzes the volatility of Shanghai stock market in China according to the expected value of posterior parameters.Regarding the sampling method of posterior distribution,this paper introduces Hamilton dynamical system and proposes HMC sampling method based on synthetic likelihood(HMCsl)by referring to MHs1 algorithm.HMC sampling method is a Metropolis algorithm based on Hamiltonian dynamic process,which uses the gradient of target probability density function,can explore the rest of the posterior distribution support domain,and also can guide the iteration to find the correct direction faster.In this paper,the HMCs1 algorithm was applied to the generalized linear regression model.The experimental results show that the HMCs1 algorithm can reduces the random walk behavior of MCMC sampling effectively,and also can approach the truth value quickly,and is less affected by the initial value,and has good convergence.