论文标题
MATDRAM：纯Matlab延迟反应自适应大都会杂货
MatDRAM: A pure-MATLAB Delayed-Rejection Adaptive Metropolis-Hastings Markov Chain Monte Carlo Sampler
论文作者
论文摘要
马尔可夫链蒙特卡洛（MCMC）算法被广泛用于数学目标函数的随机优化，采样和整合，特别是在贝叶斯反问题和参数估计的情况下。几十年来，MCMC模拟中选择的算法一直是大都会杂货（MH）算法。对传统MH-MCMC采样器的进步是延迟反应自适应大都市（DRAM）。在本文中，我们介绍了MATLAB中的Matdram，一种随机优化，采样和Monte Carlo Integration Toolbox，它实现了DRAM算法的变体，用于探索数据科学学习，机器学习和科学方面的贝叶斯模型后分布的任意维度的数学目标功能。 MATDRAM的设计目标包括MCMC模拟的几乎完整自动化，用户友好性，完全确定性的可重复性以及模拟的重新启动功能。我们还讨论了一种技术的实现详细信息，以自动监视并确保DRAM算法的提案分布的适应减少，并有效地存储所得的模拟Markov链的方法。 MATDRAM库是开源的，MIT许可的，并且是https://github.com/cdslaborg/paramonte的Paramonte库的一部分。
Markov Chain Monte Carlo (MCMC) algorithms are widely used for stochastic optimization, sampling, and integration of mathematical objective functions, in particular, in the context of Bayesian inverse problems and parameter estimation. For decades, the algorithm of choice in MCMC simulations has been the Metropolis-Hastings (MH) algorithm. An advancement over the traditional MH-MCMC sampler is the Delayed-Rejection Adaptive Metropolis (DRAM). In this paper, we present MatDRAM, a stochastic optimization, sampling, and Monte Carlo integration toolbox in MATLAB which implements a variant of the DRAM algorithm for exploring the mathematical objective functions of arbitrary-dimensions, in particular, the posterior distributions of Bayesian models in data science, Machine Learning, and scientific inference. The design goals of MatDRAM include nearly-full automation of MCMC simulations, user-friendliness, fully-deterministic reproducibility, and the restart functionality of simulations. We also discuss the implementation details of a technique to automatically monitor and ensure the diminishing adaptation of the proposal distribution of the DRAM algorithm and a method of efficiently storing the resulting simulated Markov chains. The MatDRAM library is open-source, MIT-licensed, and permanently located and maintained as part of the ParaMonte library at https://github.com/cdslaborg/paramonte.
