贝叶斯参数估计 [Bayesian Parameter Estimation]
定义: 一种贝叶斯方法，利用似然函数，通过新的证据（即观测数据）更新关于模型参数的先验信念（即先验分布），从而估计参数值并最终得到后验分布。后验分布可通过多种方式进行概括，包括：点估计（后验概率分布的均值、众数或中位数）、具有明确边界的区间，以及具有明确概率质量的区间（通常称为可信区间）。在后续估计中，后验分布还可以作为新的先验分布。此外，可以通过蒙特卡洛马尔可夫链方法对后验分布进行采样，以评估复杂模型的不确定性（例如，Foreman-Mackey et al., 2013）。
相关术语: Bayes Factor, Bayesian inference, Bayesian statistics, Null Hypothesis Significance Testing (NHST)
参考文献:
- Foreman-Mackey, D., Hogg, D. W., Lang, D., & Goodman, J. (2013). emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific, 125(925), 306–312. https://doi.org/10.1086/670067
- McElreath, R. (2020). Statistical rethinking: A Bayesian course with examples in R and Stan (2nd ed.). Taylor.
- Press, W. (2007). Numerical recipes: the art of scientific computing, 3rd edition.
- Huber, C. (2016). Introduction to Bayesian statistics, part 2: MCMC and the Metropolis–Hastings algorithm. In The Stata Blog. https://blog.stata.com/2016/11/15/introduction-to-bayesian-statistics-part-2-mcmc-and-the-metropolis-hastings-algorithm/
原稿作者: Alaa AlDoh
审阅者: Mahmoud Elsherif, Helena Hartmann, Dominik Kiersz, Meng Liu, Ana Todorovic, Markus Weinmann
翻译者: AI-driven translation tool "TransFlow" (developed by Jinbiao Yang and COSN OpenTransfer team)
译稿审阅者: Cathy Fang, Liangjie Chen, Ruoting Liu, Shuxian Jin