科学与数学jeremykun.com
没有废话的马尔可夫链蒙特卡洛（2015）
Markov chain Monte Carlo without the bullshit (2015)
2015 — 2025，它一次次回到首页
黑点是上首页（≥ 50 分）的那次投稿，空心点是没冲上去的投稿，点越大分数越高。
导读
这篇博文用通俗的语言讲解马尔可夫链蒙特卡洛（MCMC）方法：作者先引用一段晦涩难懂的百科全书式定义，然后剥掉术语外壳，解释其核心思想——通过构造马尔可夫链来高效地从复杂分布中抽样。文章多次登上 Hacker News 首页，是统计学入门的经典科普。
为什么经久不衰：它把一个以术语晦涩著称的统计学概念讲得人人能懂，多年来反复被推荐，至今仍是理解 MCMC 的最佳入门读物之一。
HN 评论精选
统计学术语混乱、社区孤立，而计算机科学正通过统一概念和实际应用接管其话语权。
21 世纪，统计学以一种前所未有的方式被推到了聚光灯下。以前从业者各自孤立，像划船几天才能互通的小岛，术语混乱，连科班出身的人读教科书都要先弄清其内部术语。我认为这正是计算机科学能抢走统计学风头的原因：它在重新组织这些概念，而且大家都关心结果（图像生成、计算机视觉等），因此获得了广泛采用。有趣的是，我觉得作者引用的那段 MCMC 定义还挺清楚的，这对我来说很少见。
madrox查看英文原文
In the 21st century, statistics has had the odd distinction of being thrust into the spotlight in a way that it never has before in its centuries of existence. Before now, practitioners have mostly been on an island...or more like several islands that are multi-day journeys from each other by rowboat. It's created weird terminology, and even the initiated don't all use the same jargon. I have a degree in statistics, and one thing I learned in school is that if you pick up a textbook the first thing you have to do is figure out its internal terminology. Only the basest concepts or ones named after people tended to use the same names everywhere. I think this is why computer science has been so successful at co-opting a lot of statistic's thunder. It's reorganizing a lot of concepts, and because everyone is interested in the results (image generation, computer vision, etc) it's getting a lot of adoption. Amusingly, I thought that the blurb on MCMC the author quoted was pretty clear. That doesn't happen to me often.
推荐 Çinlar 的教材，并用真实工作案例说明蒙特卡洛方法用采样绕开巨大状态空间的威力。
《生物统计学百科全书》里那段引文充斥着未定义的术语。真正干净、逻辑清晰、定义完备的是 Çinlar 的《随机过程导论》。当年我在一家做美国国家安全的公司读研时，曾遇到评估核潜艇舰队在特定核战争场景下生存能力的问题，限期两周。我基于 Çinlar 的书，用泊松过程支配的马尔可夫过程建模，写代码生成 500 条样本路径取平均，用强大数定律得到期望估计。一位著名概率论学家评审时质疑软件无法处理巨大的状态空间，我回答：蒙特卡洛把算力用在关键之处。
graycat查看英文原文
The quote from the article in Encyclopedia of Biostatistics is awash in undefined terminology sometimes about peripheral issues. Clean, logical, all terms well defined and explained, with plenty of advanced content, is in (with some markup using TeX) Erhan \c Cinlar, {\it Introduction to Stochastic Processes,\/} ISBN 0-13-498089-1, Prentice-Hall, Englewood Cliffs, NJ, 1975.\ \ The author was long at Princeton. He is a high quality guy. As I was working my way through grad school in a company working on US national security, a question came up about the survivability of the US SSBN fleet under a special scenario of global nuclear war but limited to sea. Results were wanted in two weeks. So, I drew from Çinlar's book, postulated a Markov process subordinated to a Poisson process, typed some code into a text editor, called a random number generator I'd written in assembler based on the recurrence X(n+1) = X(n) 5^15 + 1 mod 2^47 and was done on time. A famous probabilist was assigned to review my work. His first remark was that there was no way for my software to "fathom" the enormous "state space". I responded, at each time t, the number of SSBNs left is a random variable, finite, with an expectation. So, I generate 500 sample paths, take their average, use the strong law of large numbers, and get an estimate of their expected value within a "gnat's ass" nearly all the time. "The Monte Carlo puts the effort where the action is." The probabilist's remark was "That is a good way to think of it." Need to do some work with Markov chains, simulation, etc.? Right, just read some Çinlar, not much in prerequisites (he omitted measure theory), get clear explanations, no undefined terminology, from first principles to some relatively advanced material, and be successful with your project.
推荐一个讲解 MCMC 与 HMC 基础概念的视频。
最近看了一个关于哈密顿蒙特卡洛（HMC）的视频，它对 MCMC 以及后来的 HMC 的基本概念和动机是非常好的入门材料。
leecarraher查看英文原文
Recently watched this on Hamiltonian Monte Carlo, and it was a fantastic primer on the basic concepts and motivations of mcmc, and later hmc https://youtu.be/pHsuIaPbNbY
读者提问：'高效抽样'的确切含义是什么。
作为一个 30 年前学过统计又几乎全忘了的人，我理解了文章的全部内容，除了'我想高效地从这个分布中抽取一个样本'这一句——什么才算高效的抽样？
shafoshaf查看英文原文
As someone who took statistics 30 years ago and promptly forgot most of it, I followed everything except "I want to efficiently draw a name from this distribution". What makes a drawing efficient?
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