We introduce new affine invariant ensemble Markov chain Monte Carlo (MCMC) samplers that are easy to construct and improve upon existing methods, especially for high-dimensional problems. We first propose a simple derivative-free side move sampler that improves upon popular samplers in the \texttt{emcee} package by generating more effective proposal directions. We then develop a class of derivative-based affine invariant ensemble Hamiltonian Monte Carlo (HMC) samplers based on antisymmetric preconditioning using complementary ensembles, which outperform standard, non-affine-invariant HMC when sampling highly anisotropic distributions. We provide asymptotic scaling analysis for high-dimensional Gaussian targets to further elucidate the properties of these affine invariant ensemble samplers. In particular, with derivative information, the affine invariant ensemble HMC can scale much better with dimension compared to derivative-free ensemble samplers.

翻译：本文提出了一系列易于构建且性能优于现有方法的新型仿射不变集成马尔可夫链蒙特卡洛（MCMC）采样器，尤其适用于高维问题。我们首先提出一种简单的无导数侧向移动采样器，通过生成更有效的提议方向，改进了 \texttt{emcee} 包中常用采样器的性能。随后，我们基于互补集成与反对称预处理技术，发展了一类基于导数的仿射不变集成哈密顿蒙特卡洛（HMC）采样器，在采样高度各向异性分布时，其表现优于标准的非仿射不变HMC方法。我们针对高维高斯目标分布提供了渐近缩放分析，以进一步阐明这些仿射不变集成采样器的特性。特别地，在利用导数信息时，相较于无导数集成采样器，仿射不变集成HMC能够随维度增加展现出更优越的缩放性能。