论文标题
贝叶斯反问题上的普遍平行回火
Generalized Parallel Tempering on Bayesian Inverse Problems
论文作者
论文摘要
在当前的工作中，我们提出了平行回火算法的两个概括，灵感来自所谓的连续时间无限交换算法。这种方法发现了其起源于分子动力学群落，可以理解为连续平行回火算法的极限情况，其中两个平行链之间的状态之间的（随机）时间为零。因此，链之间之间的交换状态连续发生。在当前的工作中，我们将此思想扩展到了时间散落的马尔可夫链的背景，并呈现了两个马尔可夫链蒙特卡洛算法，这些算法遵循与连续时间无限交换过程相同的范式。我们根据其光谱差距分析了这种离散时间算法的收敛属性，并将其实施以从不同的目标分布中进行采样。数值结果表明，所提出的方法在更传统的采样算法（例如随机行走都会和（传统）平行回火）上显着改善。
In the current work we present two generalizations of the Parallel Tempering algorithm, inspired by the so-called continuous-time Infinite Swapping algorithm. Such a method, found its origins in the molecular dynamics community, and can be understood as the limit case of the continuous-time Parallel Tempering algorithm, where the (random) time between swaps of states between two parallel chains goes to zero. Thus, swapping states between chains occurs continuously. In the current work, we extend this idea to the context of time-discrete Markov chains and present two Markov chain Monte Carlo algorithms that follow the same paradigm as the continuous-time infinite swapping procedure. We analyze the convergence properties of such discrete-time algorithms in terms of their spectral gap, and implement them to sample from different target distributions. Numerical results show that the proposed methods significantly improve over more traditional sampling algorithms such as Random Walk Metropolis and (traditional) Parallel Tempering.
