The Apogee to Apogee Path Sampler
提出一种新的马尔可夫链蒙特卡洛算法AAPS，利用路径上势能局部最大点的不变性构造路径，在保持与哈密顿蒙特卡洛相近效率的同时，对调参更鲁棒。
Among Markov chain Monte Carlo algorithms, Hamiltonian Monte Carlo (HMC) is often the algorithm of choice for complex, high-dimensional target distributions; however, its efficiency is notoriously sensitive to the choice of the integration-time tuning parameter. When integrating both forward and backward in time using the same leapfrog integration step as HMC, the set of apogees, local maxima in the potential along a path, is the same whatever point (position and momentum) along the path is chosen to initialize the integration. We present the Apogee to Apogee Path Sampler (AAPS), which uses this invariance to create a simple yet generic methodology for constructing a path, proposing a point from it and accepting or rejecting that proposal so as to target the intended distribution. We demonstrate empirically that AAPS has a similar efficiency to HMC but is much more robust to the setting of its equivalent tuning parameter, the number of apogees that the path crosses. Supplementary materials for this article are available online.