Methodology and theory for unbiased MCMC.

随着硅的功率和热量达到极限，现代计算正朝着更高的并行性发展。快速计算主要是通过使用多个独立的处理器来实现的，这些处理器分开并同时执行计算任务。这对统计计算的黄金标准马尔可夫链蒙特卡罗提出了挑战，这是一个内在的顺序过程。最近提出的一种方法使马尔可夫链蒙特卡罗的原则性并行处理成为可能，并提供了克服这一挑战的可能性。虽然实现简单，但该方法可能会产生巨大的计算开销，除非可用处理器的数量在数千甚至更多，否则它是不可行的。本项目旨在增强上述方法的实用性，使其即使在处理器数量在数十或数百的情况下也能与其他方法竞争。重点是：1)通过直接改进或应用后处理技术，减少计算开销；2)通过理论分析，为新方法的最佳性能制定实用指导方针。该项目中开展的工作将对从业者和研究人员有用，他们依靠模拟从他们的统计模型中得出结论，贯穿整个科学、技术、工程和数学领域。

As the power and thermal limits of silicon are being reached, modern computing is moving towards increased parallelism. Fast computation is primarily achieved through the usage of many independent processors, which split up and perform the computation task simultaneously. This poses a challenge for Markov chain Monte Carlo, the gold standard of statistical computing, which is an inherently sequential procedure.A recently-proposed methodology enables principled parallel processing for Markov chain Monte Carlo and offers the potential to overcome this challenge. While straightforward to implement, the method may incur a significant computational overhead, rendering it impracticable unless the number of available processors is in the order of thousands, or even more.This project aims to enhance the practicality of the aforementioned methodology, making it competitive with other methods even when the number of processors is in the tens or hundreds. The focus is on: 1) reducing the computational overhead, either through direct refinements or by applying post-processing techniques, and 2) producing practical guidelines for the optimal performance of the new methodology, through theoretical analyses. The work undertaken in this project will be of use to practitioners and researchers who rely on simulation to draw conclusions from their statistical models, throughout science, technology, engineering, and mathematics.In partnership with University College Dublin (Ireland).