Novel Monte Carlo methods to generate samples from a target distribution, such as a posterior from a Bayesian analysis, have rapidly expanded in the past decade. Algorithms based on Piecewise Deterministic Markov Processes (PDMPs), non-reversible continuous-time processes, are developing into their own research branch, thanks their important properties (e.g., correct invariant distribution, ergodicity, and super-efficiency). Nevertheless, practice has not caught up with the theory in this field, and the use of PDMPs to solve applied problems is not widespread. This might be due, firstly, to several implementational challenges that PDMP-based samplers present with and, secondly, to the lack of papers that showcase the methods and implementations in applied settings. Here, we address both these issues using one of the most promising PDMPs, the Zig-Zag sampler, as an archetypal example. After an explanation of the key elements of the Zig-Zag sampler, its implementation challenges are exposed and addressed. Specifically, the formulation of an algorithm that draws samples from a target distribution of interest is provided. Notably, the only requirement of the algorithm is a closed-form function to evaluate the target density of interest, and, unlike previous implementations, no further information on the target is needed. The performance of the algorithm is evaluated against another gradient-based sampler, and it is proven to be competitive, in simulation and real-data settings. Lastly, we demonstrate that the super-efficiency property, i.e. the ability to draw one independent sample at a lesser cost than evaluating the likelihood of all the data, can be obtained in practice.
翻译:从目标分布中采集样本的方法,如巴伊西亚分析的后端分析,在过去十年中迅速扩展。基于PDMP取样员的PDMP进程(PDMPs),不可逆的连续时间进程,不可逆的连续时间进程,正在发展成自己的研究分支,这要归功于它们的重要特性(例如,正确的不变化分布、偏向性和超效率)。然而,实践没有跟上该领域的理论,使用PDMPs来解决应用问题的做法并不普遍。这首先可能是由于基于PDMP抽样员的PDMP进程(PDMPs)的一些执行背景挑战,其次是因为缺乏展示应用环境中的方法和实施情况的文件。在这里,我们用最有前途的PDMPs、Zig-Zag取样员之一,作为典型例子来解决这些问题。在解释Zig-Zag取样员的关键要素后,其实施挑战并不普遍。 具体地说,基于PDMPPDMP的样本采集到的实施成本,其目标的精确度的精确性能度的设定是从先前的精确性能到现在的精确性能的精确性数据。在评估中,对一个目标的精确性值的精确性能的精确性能的计算是另一个。我们所提供的利益。在评估中可以进一步解释。在评估中可以证明。在对一个目标的精确性能上的精确性能的计算中提供。我们提供。