利用统计力学改进现实中的贝叶斯推断：一种结合温后验和王-兰道采样的新方法
Using Statistical Mechanics to Improve Real-World Bayesian Inference: A New Method Combining Tempered Posteriors and Wang-Landau Sampling
AI总结：
本文提出一种简单方法，通过统计力学语言重新表述贝叶斯定理，结合温后验和王-兰道采样，提升贝叶斯推断质量，应用于材料科学中的方程状态建模问题。
摘要：
我们提出一种简单方法，以获得最优后验分布并减少人力和计算努力，提升贝叶斯推断质量。贝叶斯定理被重新表述为统计力学语言，其中改进的后验——称为温后验——被定义为类似于温度为τ的canonical概率分布。王-兰道采样用于获得后验概率的密度状态，从单次模拟中提取类似于相变信号的特征。此外，相变温度容易被识别，为温后验提供最佳预测性能。我们在材料科学中的现实问题（方程状态建模）中演示了该方法的有效性，该问题具有杂乱的数据、高维和相关输入参数空间以及模型输出间的“摩擦”问题。
英文摘要：
We present a simple method to obtain optimal posterior distributions and improve the quality of Bayesian inference with reduced human and computational effort. Bayes' Theorem is reformulated in the language of statistical mechanics, wherein an improved posterior -- referred to as a tempered posterior -- is defined analogously to a canonical probability distribution at temperature $τ$. Wang-Landau sampling is used to obtain the density of states of the posterior probability, and signals analogous to those of phase transitions are extracted from a single simulation. In addition, the transition temperature is easily identified, providing the tempered posterior with optimal predictive performance. We demonstrate the efficacy of the method on a real-world problem in materials science (equation of state modeling) with messy data, a high-dimensional and correlated input parameter space, and "frustration" among model outputs.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
