数学2018web.ipac.caltech.edu
21 世纪的贝叶斯定理
Bayes’ Theorem in the 21st Century (2013)
入门 · 约 45 分钟读完前置知识：基础概率论、统计学基础概念
导读
这是 Bradley Efron 2013 年发表在 Science 上的文章，回顾贝叶斯定理在 21 世纪统计学中的地位，讨论贝叶斯方法与频率学派方法各自的适用场景及现代计算技术带来的复兴。
HN 关注点：贝叶斯 vs 频率学派之争是 HN 上长盛不衰的话题，读者围绕证据的表述方式、概率的哲学解释以及现代贝叶斯计算工具展开讨论。
HN 评论精选
这几条评论里：支持 1 补充 3
补充主张论文应报告似然比（证据强度）而非后验结论，p 值不等于确定性
实验的主要目的是收集证据。结合先验信念可以得到后验信念，但最重要的是实验提供了多少证据。论文最好直接报告'实验提供了 20dB 的证据支持 A 错误、B 正确'，而不是'B 正确（p<0.01）'——百分之一的偶然并非不可能发生。分享似然比而非后验信念，也能让争论不那么激烈。第一次掷骰子就掷出双幺，并不能说明骰子被动了手脚，那只提供约 15dB 的证据。
loup-vaillant查看英文原文
http://www.overcomingbias.com/2009/02/share-likelihood-ratios-not-posterior-beliefs.html Seriously, the main point of an experiment is to gather evidence. Coupled with prior beliefs, you get a posterior belief, but the most important point is how much evidence the experiment provides. Sure, a full fledged posterior belief is needed to make an actual decision, like, what should we test next. And if a subject is deemed important enough that we need to be certain, we can replicate until we get enough evidence to trump any reasonable prior belief. (Mind publication bias, though, some replications are going to fail, and that's relevant evidence too.) In the mean time, it would be nice if the papers just told "the experiment provides 20dB of evidence that A is wrong, and B is right", instead of saying "B is right (at p<0.01)". No you're not certain B is right just yet. Your evidence is significant, perhaps even decisive, but it is not certain. A one in a hundred fluke is not unheard of. Also, sharing likelihood ratios (instead of posterior beliefs) makes the whole debate a bit less heated. Getting a double one on dice you just threw for the first time doesn't mean they are loaded to make you lose. It only provides about 15 decibels of evidence in favour of such a con job.
支持认为凭借 MCMC 和变分推断等现代计算进展，贝叶斯推断将成为默认方法
我真心相信贝叶斯推断是 21 世纪的统计学。MCMC（如 NUTS、Stan）和变分推断（如 ADVI、VAE）的最新进展加上前所未有的算力，预示着贝叶斯推断将成为默认推断引擎的近未来。先验分布是为模型加入正则化和领域知识的优美而合乎逻辑的机制。
xcodevn查看英文原文
I truly believe that Bayesian inference is the statistics of the 21st century. Recent advances in MCMC (e.g., NUTS, Stan [1]) and variational inference (e.g., ADVI [2], VAE [3], etc.) + more computing power than ever promise a near future in which Bayesian inference is the default inference engine. Prior distribution is a beautiful and logical mechanism for adding regularization, domain-specific knowledge to our model. [1] Stan, a platform for statistical modeling http://mc-stan.org/ [2] Automatic Differentiation Variational Inference https://arxiv.org/abs/1603.00788 [3] Auto-Encoding Variational Bayes https://arxiv.org/abs/1312.6114
补充认为两派是不同工具而非对错之分，关键区别在于概率的主观与客观解释
我认为这篇文章遗漏了贝叶斯与频率学派最重要的区别：概率的主观解释与频率解释。在我看来两者都不是'真理'，只是不同用途的不同工具。贝叶斯推断适合做决策（如一致性论证和完全类定理所示），其估计量也常有很好的频率性质；但贝叶斯陈述本质上 tied 于个人信念，缺乏科学所期望的客观性。频率学派关注最坏情况风险，更偏保守但可能过于悲观。真正的赢家是了解自己工具的人。
nickhuh查看英文原文
I think this article omits the most important distinction between Bayesian and Frequentist statistics: subjective vs. frequentist interpretations of probability. In my own opinion, neither is "true", they're both just different tools for different purposes. Bayesian inference is great when you have to make a decision and there are many theorems that illustrate this (for example, the arguments around coherence [1] and the complete class theorems [2]). In fact, Bayesian techniques are often useful for creating estimators with great frequentist properties! However, Bayesian interpretations of probability, and thereby the meaning of Bayesian statements, are inherently tied to the beliefs of an individual. That means that Bayesian statements usually aren't "true" in the objective / non-relative sense that we often expect from science. On the other hand, frequentist statements tend to have more of an objective flavor. The trick is: all our mathematical models have short comings and ways in which they're wrong when applied to any particular situation -- so neither really has a claim to being true. The frequentist perspective often looks at worst case risk and tends to give a more global understanding of a procedure in terms of "how does this procedure shake out in all reasonably possible scenarios?". So, frequentist methods tend to be a bit more risk-averse which is often useful but can cost you for being to pessimistic. Ultimately, the real win is to know your tools well and to pick the right one for the job. [1] https://en.wikipedia.org/wiki/Coherence_(philosophical_gambling_strategy) [2] https://projecteuclid.org/euclid.aoms/1177730345
补充推荐免费入门书籍 Think Bayes
推荐 Think Bayes，面向会编程（Python）的读者的免费电子书，是贝叶斯统计的友好入门，不必一上来就啃数学。
dna_polymerase查看英文原文
For those who are new to Bayesian Statistics and not to eager to dive into the maths right away I recommend Think Bayes [0]. It gives a nice introduction for those who know programming (Python). The ebook is available for free (see link). [0]: https://greenteapress.com/wp/think-bayes/
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