Merge branch 'main' of github.com:maxbiostat/BayesianStatisticsCourse

Author: maxbiostat

README.md

@@ -1,8 +1,6 @@
 # Bayesian Statistics
 A PhD-level course at [EMAp](https://emap.fgv.br/en).
 
-Syllabus [here](https://emap.fgv.br/disciplina/doutorado/estatistica-bayesiana) and tentative programme [here](https://docs.google.com/spreadsheets/d/1kuE-_NeSQzaBNnWc9vezXSbKfSIGQoLdmmb2zRDbOng/edit?usp=sharing). 
-
 To compile the [slides](https://github.com/maxbiostat/BayesianStatisticsCourse/blob/main/slides/bayes_stats.pdf), you'll need to do
 
 ```bash
@@ -17,7 +15,8 @@ a few times to get it right.
 
 # Books
 - [The Bayesian Choice](https://link.springer.com/book/10.1007/0-387-71599-1) (BC) by [Christian Robert](https://stats.stackexchange.com/users/7224/xian) will be our main source.
-- [A first course in Bayesian statistical methods](https://pdhoff.github.io/book/) (FC) by [Peter Hoff](https://stat.duke.edu/research/hoff#:~:text=Hoff,-Professor%20of%20Statistical&text=Peter%20Hoff%20develops%20statistical%20methodology,area%20inference%2C%20and%20multigroup%20analysis.) is a good all-purpose introduction. 
+- [A first course in Bayesian statistical methods](https://pdhoff.github.io/book/) (FC) by [Peter Hoff](https://stat.duke.edu/research/hoff#:~:text=Hoff,-Professor%20of%20Statistical&text=Peter%20Hoff%20develops%20statistical%20methodology,area%20inference%2C%20and%20multigroup%20analysis.) is a good all-purpose introduction.
+- [Theory of Statistics](https://link.springer.com/book/10.1007/978-1-4612-4250-5) (SV) by [Mark Schervish](https://www.cmu.edu/dietrich/statistics-datascience/people/faculty/mark-schervish.html) is a comprehensive reference. 
 - [Bayesian Theory](https://onlinelibrary.wiley.com/doi/book/10.1002/9780470316870) (BT) by [José Bernardo](https://www.uv.es/bernardo/) and [Adrian Smith](https://en.wikipedia.org/wiki/Adrian_Smith_(statistician)) is a technical behemoth, suitable for use as a reference guide. 
 
 # Resources
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 - [Awesome Bayes](https://github.com/hectormz/awesome-bayes) is a curated list of bayesian resources, including blog posts and podcasts.
 
 ### Acknowledgements
-[Guido Moreira](http://github.com/GuidoAMoreira/) suggested topics, exercises and exam questions.
+[Guido Moreira](http://github.com/GuidoAMoreira/) and [Isaque Pim](https://github.com/isaquepim) suggested topics, exercises and exam questions.
+[Lucas Moschen](https://github.com/lucasmoschen) made many good suggestions. 
+
+# Exercises
+
+We keep a list [here](https://github.com/maxbiostat/BayesianStatisticsCourse/blob/main/exercises/BC_exercises.md). I recommend you check back every so often because this is likely to be updated (if infrequently). 
+- **2024-03-24**: Exercises about Chapters 1 and 2 are up.
 
 # Syllabus
 ## Lecture 0: Overview
@@ -45,7 +50,8 @@ a few times to get it right.
 - Berger and Wolpert's 1988 [monograph](https://errorstatistics.files.wordpress.com/2016/04/berger-wolpert-1988.pdf) is the definitive text on the [Likelihood Principle](https://en.wikipedia.org/wiki/Likelihood_principle) (LP).
 - See [this](https://arxiv.org/pdf/1906.10733.pdf) paper By Franklin and Bambirra for a generalised version of the LP.
 - As advanced reading, one can consider [Birnbaum (1962)](https://www.tandfonline.com/doi/abs/10.1080/01621459.1962.10480660) and a helpful review [paper](https://link.springer.com/content/pdf/10.1007/978-1-4612-0919-5_31.pdf) published 30 years later by Bjornstad.
-- Michael Evans has a few papers on the LP. See [Evans, Fraser & Monette (1986)](https://errorstatistics.files.wordpress.com/2017/12/evans-fraser-monette-1986.pdf) for an argument using a stronger version of CP and [Evans, 2013](https://projecteuclid.org/journals/electronic-journal-of-statistics/volume-7/issue-none/What-does-the-proof-of-Birnbaums-theorem-prove/10.1214/13-EJS857.full) for a flaw with the original 1962 paper by Birnbaum. 
+- Michael Evans has a few papers on the LP. See [Evans, Fraser & Monette (1986)](https://errorstatistics.files.wordpress.com/2017/12/evans-fraser-monette-1986.pdf) for an argument using a stronger version of CP and [Evans, 2013](https://projecteuclid.org/journals/electronic-journal-of-statistics/volume-7/issue-none/What-does-the-proof-of-Birnbaums-theorem-prove/10.1214/13-EJS857.full) for a flaw with the original 1962 paper by Birnbaum.
+- Deborah G. Mayo [challenged](https://projecteuclid.org/journals/statistical-science/volume-29/issue-2/On-the-Birnbaum-Argument-for-the-Strong-Likelihood-Principle/10.1214/13-STS457.full) Birnbaum's argument on the LP. But Mayo implicitly changed the statement of the SP, nullifing her point. This [Cross-Validate](https://stats.stackexchange.com/questions/379798/did-deborah-mayo-refute-birnbaums-proof-of-the-likelihood-principle) post adds more details to the story and to the relevance of the LP.
 
 ## Lecture 2: Belief functions, coherence, exchangeability
 
@@ -75,6 +81,7 @@ a few times to get it right.
 
 **Optional reading**
 - [This](https://arxiv.org/pdf/1303.5973.pdf) paper by Christian Robert gives a nice discussion of the Jeffreys-Lindley paradox.
+- [This](https://link.springer.com/content/pdf/10.1007/s00407-022-00298-3.pdf) paper by [Wagenmakers](https://www.ejwagenmakers.com/) is an excellent historical account of the paradox, and clears many misconceptions. 
 - [Jaynes](https://en.wikipedia.org/wiki/Edwin_Thompson_Jaynes)'s 1976 monograph [Confidence Intervals vs Bayesian Intervals](https://link.springer.com/chapter/10.1007/978-94-009-6581-2_9) is a great source of useful discussion. [PDF](https://link.springer.com/content/pdf/10.1007/978-94-010-1436-6_6.pdf).
 
 ## Lecture 7: Bayesian Testing II

exercises/BC_exercises.md

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+## Exercises from [The Bayesian Choice](https://link.springer.com/book/10.1007/0-387-71599-1)
+
+### Ch 1
+1.1, 1.2, 1.3, 1.4, 1.5, 1.9, 1.10, 1.15, 1.17, 1.24, 1.25, 1.26, 1.29, 1.32, 1.33, 1.34, 1.35, 1.36, 1.39, 1.40, 1.43, 1.47, 1.48, 1.50, 1.51, 1.53, 1.55, 1.62.
+### Ch 2
+2.2, 2.6, 2.11, 2.16, 2.18, 2.19, 2.20, 2.23, 2.24, 2.28, 2.31, 2.43, 2.49, 2.51.
+### Ch 3
+3.2, 3.9, 3.11, 3.18, 3.21, 3.27, 3.28, 3.30, 3.43, 3.51, 3.53, 3.57, 3.59.
+### Ch 4
+4.2, 4.5, 4.12, 4.14, 4.15, 4.19, 4.25, 4.26, 4.33, 4.51.
+### Ch 5
+5.2, 5.3, 5.9, 5.10, 5.11, 5.15, 5.19, 5.25, 5.26, 5.35, 5.42, 5.47, 5.51.
+### Ch 6
+### Ch 7
+7.1, 7.10, 7.12, 7.28, 7.31, 7.32, 7.33, 7.34, 7.35, 7.38
+
+## Computational stuff
+1.41 (Gibbs sampling) 

slides/compile.sh

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+\subsection{Decision Theory basics}
+\begin{frame}{The decision-theoretic foundations of the Bayesian paradigm}
+ \begin{defn}[Loss function]
+ \label{def:loss_fn} 
+ \end{defn}
+\end{frame}
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+\begin{frame}{Utility functions}
+Properties:
+\end{frame}
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+\begin{frame}{}
+ \begin{theo}[]
+   \end{theo}
+ See Proposition 4.3 in \cite{Bernardo2000} for a proof outline.
+ Here we shall prove the version from~\cite{DeFinetti1931}.
+  \begin{idea}[] 
+  \end{idea}
+\end{frame}
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+\begin{frame}{Recommended reading}
+\begin{itemize}
+  \item[\faBook] \cite{Robert2007} Ch. 2. and $^\ast$\cite{Schervish2012} Ch.3;
+  \item[\faForward] Next lecture: \cite{Hoff2009} Ch. 2 and $^\ast$\cite{Schervish2012} Ch.1;
+ \end{itemize} 
+\end{frame}