Abstract:Hamilton Monte Carlo (HMC) method is a fast sampling algorithm. To sampling a Hamiltonian equation, the HMC method uses the Leapfrog integrator. As a result, the unsynchronized values of position and momentum variables of the equaiton are possibly generated during the iterative process and the resulting estimation errors can seriously damage the sampling efficiency and stability of the sampling result. To solve this problem, here we propose an improved HMC (IHMC) method by replacing the Leapfrog integrator in HMC with the Velocity Verlet integrator, The IHMC method calculates the value of both variables simutaneously in each iteration. Two numerical examples are implemented to check the performance of IHMC method, one is the problem of estiimating the parameters of realized stochastic volatility (RASV) model with asymmetric effects, the other is the problem of sampling the variance Gamma distribution. It is shown that the IHMC method has higher sampling efficiency and more stable sampling result compared with the HMC method.
