论文标题
使用速度跳跃过程确切靶向吉布斯分布
Exact targeting of Gibbs distributions using velocity-jump processes
论文作者
论文摘要
这项工作介绍和研究了一个新的速度跳跃马尔可夫过程的新家族，直接适合精确的模拟，并具有以下两个属性：i）轨迹在法律上收敛时，当时间阶段参数消失到给定的langevin或hamil-tonian动力学时； ii）该过程的固定分布始终由任何目标对数密度的高斯（对于速度）的乘积确切地给出，任何目标对数密度的梯度是computabe，以及一些其他明确的适当上限。该过程没有表现出任何速度反射（可以控制跳跃大小），并且适合“分解方法”。我们提供了一个严格的数学证明：i）小时步的收敛到汉密尔顿/兰格文动力学，以及ii）当存在适当的速度噪声时，指数的快速收敛到目标分布。数值实现已详细介绍和说明。
This work introduces and studies a new family of velocity jump Markov processes directly amenable to exact simulation with the following two properties: i) trajectories converge in law when a time-step parameter vanishes towards a given Langevin or Hamil-tonian dynamics; ii) the stationary distribution of the process is always exactly given by the product of a Gaussian (for velocities) by any target log-density whose gradient is pointwise computabe together with some additional explicit appropriate upper bound. The process does not exhibit any velocity reflections (jump sizes can be controlled) and is suitable for the 'factorization method'. We provide a rigorous mathematical proof of: i) the small time-step convergence towards Hamiltonian/Langevin dynamics, as well as ii) the exponentially fast convergence towards the target distribution when suitable noise on velocity is present. Numerical implementation is detailed and illustrated.
