MCBench: A Benchmark Suite for Monte Carlo Sampling Algorithms

作     者：Ding, Zeyu Grunwald, Cornelius Ickstadt, Katja Kröninger, Kevin La Cagnina, Salvatore 

作者机构：Department of Statistics TU Dortmund University Vogelpothsweg 87 Dortmund44227 Germany Department of Physics TU Dortmund University Otto-Hahn-Straße 4 Dortmund44227 Germany Lamarr-Institute for Machine Learning and Artificial Intelligence Joseph-von-Fraunhofer-Straße 25 Dortmund44227 Germany TU Dortmund - Center for Data Science and Simulation TU Dortmund University August-Schmidt-Straße 4 Dortmund44227 Germany 

出 版 物：《arXiv》 (arXiv)

年 卷 期：2025年

核心收录：

主　　题：Markov chains 

摘      要：In this paper, we present MCBench, a benchmark suite designed to assess the quality of Monte Carlo (MC) samples. The benchmark suite enables quantitative comparisons of samples by applying different metrics, including basic statistical metrics as well as more complex measures, in particular the sliced Wasserstein distance and the maximum mean discrepancy. We apply these metrics to point clouds of both independent and identically distributed (IID) samples and correlated samples generated by MC techniques, such as Markov Chain Monte Carlo or Nested Sampling. Through repeated comparisons, we evaluate test statistics of the metrics, allowing to evaluate the quality of the MC sampling algorithms. Our benchmark suite offers a variety of target functions with different complexities and dimensionalities, providing a versatile platform for testing the capabilities of sampling algorithms. Implemented as a Julia package, MCBench enables users to easily select test cases and metrics from the provided collections, which can be extended as needed. Users can run external sampling algorithms of their choice on these test functions and input the resulting samples to obtain detailed metrics. Copyright © 2025, The Authors. All rights reserved.