  Recently, the Hamilton Monte Carlo (HMC) has become widespread as one of the
more reliable approaches to efficient sample generation processes. However, HMC
is difficult to sample in a multimodal posterior distribution because the HMC
chain cannot cross energy barrier between modes due to the energy conservation
property. In this paper, we propose a Stochastic Approximate Hamilton Monte
Carlo (SAHMC) algorithm for generating samples from multimodal density under
the Hamiltonian Monte Carlo (HMC) framework. SAHMC can adaptively lower the
energy barrier to move the Hamiltonian trajectory more frequently and more
easily between modes. Our simulation studies show that the potential for SAHMC
to explore a multimodal target distribution more efficiently than HMC based
implementations.
