Bayes统计

• 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.

• 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.

• 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.

• computation: Jun S Liu. Monte Carlo Strategies in Scientific Computing下载 Monte Carlo Strategies in Scientific Computing. New York: Springer, 2001.

  • 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.

• 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
  • Slides: bda 1.pdf下载 bda 1.pdf
  • Resources: confidence interval estimation for binomial proportions链接到外部网站。
  • Code: normal_example_mean_only.stan下载 normal_example_mean_only.stan normal_example.stan下载 normal_example.stan lm.stan下载 lm.stan ch1.R下载 ch1.R
• 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
  • 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
• 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
    • 
• 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
  • Slides: TBA
• Bayesian Hypothesis Testing, Model Checking, Model Selection, and Model Averaging
  • Slides: TBA
  • R code: ch4.R下载 ch4.R
• Frequentist properties of Bayesian inference
  • Useful resources: 
  • Slides: TBA
  • R code: ch5.R下载 ch5.R
• Hierarchical Bayesian models
  • Useful resources: 
    • nan laird interview.pdf下载 nan laird interview.pdf
    • laird ware 1982.pdf下载 laird ware 1982.pdf
  • Slides: TBA
• 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
  • Slides: TBA