论文标题
哈密顿蒙特卡洛的设计，以完美模拟一般连续分布
Design of Hamiltonian Monte Carlo for perfect simulation of general continuous distributions
论文作者
论文摘要
汉密尔顿蒙特卡洛（HMC）是一种模拟平滑分布的有效方法，并激发了广泛使用的NO-U-Turn采样器（螺母）和软件stan。我们基于坚果和“无偏抽样”的技术来设计HMC算法，这些HMC算法可以完美地模拟HMC适合的一般连续分布。我们的方法使马尔可夫链蒙特卡洛收敛误差与实验误差的分离，因此与当前最新的摘要统计数据相比，它提供了更强大的MCMC收敛诊断，该统计数据混淆了这两个错误。不同MCMC算法的客观比较由每个完美样本点的衍生化评估数量提供。我们证明了使用普通，$ t $的应用和高达100个维度的普通混合物分布以及12维贝叶斯套索回归的方法。 HMC有效地运行，每个轨迹的目标为20至30分。每个完美样本点的衍生品评估范围从单变量正态分布的390到12,000，对于两种正态分布的100维混合物，其模式为6个标准偏差，为22,000，100维$ t $ t $ distribution具有4度的自由度。
Hamiltonian Monte Carlo (HMC) is an efficient method of simulating smooth distributions and has motivated the widely used No-U-turn Sampler (NUTS) and software Stan. We build on NUTS and the technique of "unbiased sampling" to design HMC algorithms that produce perfect simulation of general continuous distributions that are amenable to HMC. Our methods enable separation of Markov chain Monte Carlo convergence error from experimental error, and thereby provide much more powerful MCMC convergence diagnostics than current state-of-the-art summary statistics which confound these two errors. Objective comparison of different MCMC algorithms is provided by the number of derivative evaluations per perfect sample point. We demonstrate the methodology with applications to normal, $t$ and normal mixture distributions up to 100 dimensions, and a 12-dimensional Bayesian Lasso regression. HMC runs effectively with a goal of 20 to 30 points per trajectory. Numbers of derivative evaluations per perfect sample point range from 390 for a univariate normal distribution to 12,000 for a 100-dimensional mixture of two normal distributions with modes separated by six standard deviations, and 22,000 for a 100-dimensional $t$-distribution with four degrees of freedom.
