Bayes统计
Bayes统计
本门课程主要内容设计贝叶斯统计与统计。会争取覆盖以下内容:Bayesian vs. Frequentist philosophy, priors, hierarchical Bayesian models, applied Bayesian data analysis, sampling algorithms, variational Bayes, nonparametric and empirical Bayesian inference, Bayesian Uncertainty Quantification (UQ) for Inverse Problems related to O/PDEs or SO/PDEs.
课程邮件:
时间与地点:
每周五1-3节三节连上,东上院212
答疑:
周五课后。
其他时间可发邮件单独安排答疑时间。
TA:
王祉静 wangzhijing@sjtu.edu.cn
成绩构成:
15%上课参与, 40%平时作业(共2次), 45% 课堂小测(闭卷).
作业尽量用latex(如果不会使用非要用word也没问题,但latex熟练后实际上要比word节省时间)
小测总共5次,每次占用30/45分钟课时,目前已确定的时间为:3.14第一节(30分钟),4.11第一节(45分钟),6.6学期最后一次课的第一节(45分钟)
编程语言:
如果你更喜欢python或matlab,也可以使用。但是授课老师和助教无法对R之外的语言提供帮助。
参考资料 (均不必须):
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basic: Andrew Gelman, John B. Carlin, Hal S. Stern, David B. Dunson, Aki Vehtari, and Donald B. Rubin. Bayesian Data Analysis
链接到外部网站。. 2013.
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practice: Jean-Michel Marin and Christian P. Robert. Bayesian essentials with R
链接到外部网站。. Vol. 48. New York: Springer, 2014.
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conceptual & practice: Christian P. Robert. The Bayesian choice: from decision-theoretic foundations to computational implementation
下载 The Bayesian choice: from decision-theoretic foundations to computational implementation. Vol. 2. New York: Springer, 2007.
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computation: Jun S Liu. Monte Carlo Strategies in Scientific Computing
下载 Monte Carlo Strategies in Scientific Computing. New York: Springer, 2001.
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This book is now a bit obsolete. I highly recommend this course
链接到外部网站。 taught by Pierre Jacob from ESSEC Business School as a handy resource.
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theory: Subhashis Ghosh and Aad van der Vaart. Fundamentals of Nonparametric Bayesian Inference
下载 Fundamentals of Nonparametric Bayesian Inference. Vol. 44. Cambridge University Press, 2017.
- Bayesian inverse problems: Andrew M Stuart. Inverse problems: a Bayesian perspective
链接到外部网站。. Acta Numerica, 2010, 19: 451-559.
R的帮助资料:
1. 可以试着用R prep.R下载 R prep.R进行尝试自学
课程安排 (being updated as the semester progresses):
- Introduction & overview of the semester
- The role of priors and philosophy of statistics
- Useful resources:
- James O. Berger - Statistical Decision Theory and Bayesian Analysis.djvu
下载 James O. Berger - Statistical Decision Theory and Bayesian Analysis.djvu
- obayes-debate.pdf
下载 obayes-debate.pdf
- The interplay between Bayesian and frequentist analysis.pdf
下载 The interplay between Bayesian and frequentist analysis.pdf
- The selection of prior distributions by formal rules.pdf
下载 The selection of prior distributions by formal rules.pdf
- Conditioning, likelihood, and coherence- A review of some foundational concepts.pdf
下载 Conditioning, likelihood, and coherence- A review of some foundational concepts.pdf
- Exponential family distributions: 1176345690.pdf
下载 1176345690.pdf
- Prior elicitation: Prior knowledge elicitation- The past, present, and future.pdf
下载 Prior knowledge elicitation- The past, present, and future.pdf
- James O. Berger - Statistical Decision Theory and Bayesian Analysis.djvu
- Slides: bda 2.pdf
下载 bda 2.pdf
- Stein's paradox: James-Stein estimator proof.pdf
下载 James-Stein estimator proof.pdf
- Code: ch2.R
下载 ch2.R
- Useful resources:
- Sampling algorithms
- Useful resources: computing
- A good short tutorial on HMC (video lecture): An Introduction to Hamiltonian Monte Carlo Method for Sampling.mp4
下载 An Introduction to Hamiltonian Monte Carlo Method for Sampling.mp4
- Slides: bda 3.1.pdf
下载 bda 3.1.pdf
- Code: ch3.R
下载 ch3.R
- 一些例子:
- sd=0.01
- sd = 1
- sd = 5
- sd=0.01
- Variational inference
- Useful resources (not covered in this chapter):
- Graphical Models, Exponential Families, and Variational Inference
下载 Graphical Models, Exponential Families, and Variational Inference by Martin Wainwright & Michael I Jordan
- Notes on statistical physics
链接到外部网站。 by Subhabrata Sen & Andrea Montanari
- Graphical Models, Exponential Families, and Variational Inference
- Slides: TBA
- Useful resources (not covered in this chapter):
- Bayesian Hypothesis Testing, Model Checking, Model Selection, and Model Averaging
- Frequentist properties of Bayesian inference
- Hierarchical Bayesian models
- Bayesian nonparametrics
- Useful resources:
- modern bn.pdf
下载 modern bn.pdf
- Fundamentals of Nonparametric Bayesian Inference.pdf
下载 Fundamentals of Nonparametric Bayesian Inference.pdf by Aad van der Vaart & Subhashis Ghosal
- modern bn.pdf
- Slides: TBA
- Useful resources: