We introduce a switching Hamiltonian Monte Carlo method for sampling from finite mixture Boltzmann-Gibbs distributions. We propose symmetric numerical integrators to approximate switching Hamiltonian dynamics interlaced with Poisson jumps, where the regime-switching chain is simulated using the uniformization technique or the stochastic simulation algorithm. We prove geometric ergodicity of the resulting Markov chain. We develop an approach based on the discrete Poisson equation associated with numerical schemes to estimate the error in computing ergodic averages. Using this approach we prove that the proposed numerical integrators have second-order bias. This approach is simple and can be generalized to other settings, for example, kinetic Langevin equations. Finally, we verify the convergence result via numerical experiment.

翻译：我们提出了一种切换式哈密顿蒙特卡洛方法，用于从有限混合玻尔兹曼-吉布斯分布中抽样。我们设计了对称数值积分器来逼近与泊松跳跃交织的切换式哈密顿动力学过程，其中状态切换链采用均匀化技术或随机模拟算法进行模拟。我们证明了最终马尔可夫链的几何遍历性。基于与数值格式相关的离散泊松方程，我们发展了一种方法以估计遍历均值计算中的误差。利用该方法，我们证明了所提出的数值积分器具有二阶偏差。该框架具有简洁性，并可推广至其他场景，例如动力学朗之万方程。最后，我们通过数值实验验证了收敛性结论。