New developments in non-reversible Markov chain Monte Carlo

马尔可夫链蒙特卡罗（MCMC）算法执行的探索可以比作一些有趣的地形的探索。传统的MCMC是“可逆的”：这一条件的简单性促进了对今天可用的标准MCMC算法的大量扩展和变化;然而，可逆性也意味着在相对平坦的地形上，（并且在真实的高维应用中，只有一个方向是“上坡”，而所有其他方向相对平坦），MCMC“步行者”失去方向感，从而其路径变得不稳定，并且探索缓慢。相比之下，不可逆MCMC即使在平坦地形上也保持方向感。目前的不可逆算法主要有两种：一种是想象一架无人机在地形上方直线飞行，偶尔改变方向，以保持在较高区域的上方;另一种是颠倒地形，想象沿着它以随机方向踢沿着的球。这两种方法都有很大的潜力，但也存在限制其可用性的实际问题。利用这两种方法，该项目将创建新的不可逆算法，这些算法比标准的、可逆的MCMC算法效率高得多，可以应用于各种各样的环境;它还将为统计从业人员创建易于使用的软件。MCMC用于对各种应用中的复杂数据集进行统计分析，从金融和欺诈检测，通过了解，预测和干预传染病的传播，了解宇宙中暗物质的位置，我们的工作将使任何分析这些和许多其他领域复杂数据集的人受益。

The exploration performed by a Markov chain Monte Carlo (MCMC) algorithm can be likened to the exploration of some interesting terrain. Traditional MCMC is `reversible': the simplicity of this condition has facilitated the huge number of extensions and variations on the standard MCMC algorithm that are available today; however reversibility also implies that on relatively flat terrain (and in real, high-dimensional applications only one direction is `uphill', with all other directions relatively flat), an MCMC `walker' loses their sense of direction so that their path becomes erratic and the exploration slow. By contrast, non-reversible MCMC keeps a sense of direction even over flat terrain. Current non-reversible algorithms come in two main flavours: one imagines a drone flying in a straight line above the terrain and occasionally changing direction so as to keep above the higher regions; the other inverts the terrain and imagines kicking a ball along it in a random direction. Both of these methods have great potential, but also practical problems that limit their usability. Drawing on both methods, this project will create new non-reversible algorithms which are much more efficient than standard, reversible, MCMC and can be applied across a wide variety of contexts; it will also create easy-to-use software for statistical practitioners. MCMC is used for the statistical analysis of complex data sets across a huge range of applications, from finance and fraud detection, through understanding, predicting and intervening in the spread of infectious diseases, to understanding the location of dark matter in the universe, and our work will benefit anyone analysing complex datasets in these and many other areas.