论文标题
MCMC输出的最佳变薄
Optimal Thinning of MCMC Output
论文作者
论文摘要
使用启发式方法来评估收敛性并压缩马尔可夫链蒙特卡洛的输出，就产生的经验近似而言，可以是最佳的。通常，许多初始状态归因于“燃烧”并删除，而如果还需要压缩，则链的其余部分被“稀释”。在本文中，我们考虑回顾性从样本路径中选择固定基数的子集的问题，以使其经验分布提供的近似值接近最佳。提出了一种新的方法，基于核心stein差异的贪婪最小化，该方法适用于需要重压的问题。理论结果保证了该方法的一致性及其有效性，这在普通微分方程的参数推断的挑战性背景下得到了证明。软件可在Python，R和Matlab的Stein Thinning软件包中找到。
The use of heuristics to assess the convergence and compress the output of Markov chain Monte Carlo can be sub-optimal in terms of the empirical approximations that are produced. Typically a number of the initial states are attributed to "burn in" and removed, whilst the remainder of the chain is "thinned" if compression is also required. In this paper we consider the problem of retrospectively selecting a subset of states, of fixed cardinality, from the sample path such that the approximation provided by their empirical distribution is close to optimal. A novel method is proposed, based on greedy minimisation of a kernel Stein discrepancy, that is suitable for problems where heavy compression is required. Theoretical results guarantee consistency of the method and its effectiveness is demonstrated in the challenging context of parameter inference for ordinary differential equations. Software is available in the Stein Thinning package in Python, R and MATLAB.
