Approximate Bayesian Computation With Synthetic Likelihood

Approximate Bayesian Computation(ABC)algorithm is a kind of simulation-based Bayesian computation method developed recently.It is useftul to estimate the parameters when the likelihood function is analytically infeasible or computationally intensive.Bayesian Computation with empirical likelihood(BCel)is a refined ABC algorithm,aiming to bypass the tunning problems of ABC.Stable distribution is widely used to describe the financial data with heavy tail and excess kurtosis.Since there is no explicit density function for the stable distribution,classical parameter estimation methods are not available.Here illustrate how to use the BCel to estimate the parameters with stable distribution.And Extensive simulation study shows its good performance.Synthetic likelihood is an agent likelihood.It can be combined with Metropolis Hastings Markov Chain Monte Carlo(MH MCMC)algorithms to estimate the complex models.Similar to BCel,we combine the synthetic likelihood with ABC to propose a new method:Bayesian Computation with Synthetic Likelihood(BCsl).BCsl modifies the Metropolis Hastings Markov Chain Monte Carlo with synthetic likelihood algorithm(MHsl),avoiding tedious work on adjusting acceptance rate and being more robust than BCel.BCsl is applied to five models with data simulation,compared with BCel and MHsl,like chaotic ecological dynamic system model,quantile distribution,heteroscedastic time series model,hierarchical binomial model and hierarchical population structure and local adoption model.Finally,an empirical study one Shanghai composite index time series with BCsl is made.