Amongst 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, $T$. When integrating both forward and backward in time using the same leapfrog integration step as HMC, the set of local maxima in the potential along a path, or apogees, is the same whatever point (position and momentum) along the path is chosen to initialise the integration. We present the Apogee to Apogee Path Sampler (AAPS), which utilises 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, a non-negative integer, $K$, the number of apogees that the path crosses.
翻译:在Markov连锁的蒙特卡洛算法中,汉密尔顿·蒙特卡洛(HMC)往往是选择复杂、高维目标分布的算法;然而,其效率对集成时间调制参数($T$)的选择具有臭名昭著的敏感性。当将前向和后向都与HMC同时结合时,使用与HMC相同的跃式集成步骤时,在一条路径上(或远地点)的一套潜在的本地最大值(位置和势头)与在路径上选择的相同的调制参数(位置和势头)相同。我们向Apogee路径采样器(APS)介绍远地点(APS),我们利用它来创建一条简单而通用的方法来构建一条路径,从中提出一个点,接受或拒绝这一提议,以便瞄准预定的分布。我们从经验上表明,AAPS具有与HMC相似的效率,但对于与其相应的调制参数的设置更有力得多,即非负整整值,$K$,即路径交叉的远地点的数目。