论文标题
分裂的哈密顿蒙特卡洛重新审视
Split Hamiltonian Monte Carlo revisited
论文作者
论文摘要
我们研究了基于$ H_0（θ，P）+U_1（θ）$的Hamiltonian $ h $的汉密尔顿蒙特卡洛（HMC）采样器，其中$ h_0 $是quadratic，$ u_1 $ small。我们表明，通常，此类采样器遭受了基于标准LeapFrog积分器的算法稳定性限制的措施。可以通过预处理动力学来规避限制。数值实验表明，当$ h_0（θ，p）+u_1（θ）$分割与预处理结合时，可以构造采样器远比标准的leapfrog hmc更有效。
We study Hamiltonian Monte Carlo (HMC) samplers based on splitting the Hamiltonian $H$ as $H_0(θ,p)+U_1(θ)$, where $H_0$ is quadratic and $U_1$ small. We show that, in general, such samplers suffer from stepsize stability restrictions similar to those of algorithms based on the standard leapfrog integrator. The restrictions may be circumvented by preconditioning the dynamics. Numerical experiments show that, when the $H_0(θ,p)+U_1(θ)$ splitting is combined with preconditioning, it is possible to construct samplers far more efficient than standard leapfrog HMC.
