For several decades now, Bayesian inference techniques have been applied to theories of particle physics, cosmology and astrophysics to obtain the probability density functions of their free parameters. In this study, we review and compare a wide range of Markov Chain Monte Carlo (MCMC) and nested sampling techniques to determine their relative efficacy on functions that resemble those encountered most frequently in the particle astrophysics literature. Our first series of tests explores a series of high-dimensional analytic test functions that exemplify particular challenges, for example highly multimodal posteriors or posteriors with curving degeneracies. We then investigate two real physics examples, the first being a global fit of the $\Lambda$CDM model using cosmic microwave background data from the Planck experiment, and the second being a global fit of the Minimal Supersymmetric Standard Model using a wide variety of collider and astrophysics data. We show that several examples widely thought to be most easily solved using nested sampling approaches can in fact be more efficiently solved using modern MCMC algorithms, but the details of the implementation matter. Furthermore, we also provide a series of useful insights for practitioners of particle astrophysics and cosmology.

翻译：数十年来，贝叶斯推断技术已被应用于粒子物理、宇宙学及天体物理理论中，以获取其自由参数的概率密度函数。本研究系统评述并比较了多种马尔可夫链蒙特卡洛（MCMC）与嵌套抽样技术，旨在评估这些方法在处理粒子天体物理文献中最常见函数类型时的相对效能。第一系列测试探究了一组高维解析测试函数，这些函数体现了特定挑战，例如高度多峰的后验分布或具有弯曲简并性的后验分布。随后我们研究了两个实际物理案例：第一个是基于普朗克实验的宇宙微波背景数据对ΛCDM模型进行的全局拟合，第二个是利用各类对撞机与天体物理数据对最小超对称标准模型进行的全局拟合。研究表明，一些普遍认为最适合用嵌套抽样方法求解的案例，实际上可通过现代MCMC算法更高效地求解，但具体实现细节至关重要。此外，本研究还为粒子天体物理与宇宙学领域的实践者提供了一系列实用见解。