Updates from Overleaf

Author: maxbiostat

slides/bayes_stats.tex

@@ -118,7 +118,7 @@
 \begin{document}
 \include{lecture_0}
 \include{lecture_1}
-% \include{lecture_2}
+\include{lecture_2}
 \include{lecture_3}
 \include{lecture_4}
 \include{lecture_5}

slides/compile.sh

@@ -18,6 +18,7 @@ \section{Part I: Foundations}
  \begin{itemize}
   \item  \cite{Robert2007};
   \item \cite{Hoff2009};
+  \item  \cite{Schervish1995};
   \item \cite{Bernardo2000}.  
  \end{itemize}
 \end{itemize}

slides/lecture_0.tex

@@ -44,7 +44,7 @@ \section*{Bayesian rules}
 There is no such thing as a truly objective analysis, and taking objectivity as premise might hinder our ability to focus on actual discovery and explanation~\citep{Hennig2017}.
 \begin{idea}[The subjective basis of knowledge]
 \label{id:subjective}
- Knowledge arises from a confrontation between \texit{a prioris} and experiments (data).
+ Knowledge arises from a confrontation between \textit{a prioris} and experiments (data).
  Let us hear what Poincaré\footnote{Jules Henri Poincaré (1854--1912) was a French mathematician and the quote is from \textit{La Science and l'Hypóthese} (1902).} had to say:
  \begin{quote}
   ``It is often stated that one should experiment without preconceived ideas.

slides/lecture_11.tex

@@ -0,0 +1,26 @@
+\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}

slides/lecture_2.tex

@@ -5,7 +5,7 @@ \subsection{Belief functions and exchangeability}
 \begin{itemize}
  \item [F] = \{votes for a left-wing candidate\} ;
  \item [G] = \{is in the 10\% lower income bracket\} ;
- \item [H] = \{lives in a large\} ;
+ \item [H] = \{lives in a large city\} ;
 \end{itemize}
 
  \begin{defn}[Belief function]
@@ -19,7 +19,7 @@ \subsection{Belief functions and exchangeability}
  \begin{itemize}
   \item $\be(F) > \be(G)$ means we would bet on $F$ being true over $G$ being true;
   \item $\be(F\mid H) > \be(G \mid H)$ means that, \textbf{conditional} on knowing $H$ to be true, we would bet on $F$ over $G$;
-  \item $\be(F\mid G) > \be(F \mid H)$ means that if we were forced to be on $F$, we would be prefer doing so if $G$ were true than $H$.
+  \item $\be(F\mid G) > \be(F \mid H)$ means that if we were forced to bet on $F$, we would be prefer doing so if $G$ were true than $H$.
  \end{itemize}
 \end{frame}
 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
@@ -184,6 +184,7 @@ \subsection{Belief functions and exchangeability}
  As the exchangeability results above clearly demonstrate, being able to use conditional independence is a handy tool.
  More specifically, knowing on what to condition so as to make things exchangeable is key to statistical analysis.
  \begin{idea}[Conditioning is the soul of Statistics\footnote{This idea is due to Joe Blitzstein, who did his PhD under no other than the great Persi Diaconis.}] 
+ \label{idea:conditioning_soul}
  Knowing on what to condition can be the difference between an unsolvable problem and a trivial one.
  When confronted with a statistical problem, always ask yourself ``What do I know for sure?'' and then ``How can I create a conditional structure to include this information?''.
  \end{idea}

slides/lecture_3.tex

@@ -117,7 +117,7 @@ \section*{Bayesian point estimation}
  for $\boldsymbol{G}$ a $p \times p$ non-negative symmetric matrix.
  In this case, we get
  $$ \delta_\pi = \frac{E_p[w(\theta)\theta]}{E_p[w(\theta)]}. $$
- Please \textbf{note} that there is no universal justification for quadratic loss other than (sometimes leading to increased) mathematical tractability
+ Please \textbf{note} that there is no universal justification for quadratic loss other than (sometimes leading to increased) mathematical tractability.
 \end{frame}
 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
 \begin{frame}{Loss estimation}

slides/lecture_5.tex

@@ -82,9 +82,9 @@ \section*{Bayesian model choice}
 A nice consequence of the formulation we just saw is that the predictive distribution looks quite intuitive:
 \begin{align}
 \nonumber
- p(\tilde{x} \mid \boldsymbol{x}) &= \sum_{j} w_j \int_{\boldsymbol{\Theta}_j} f_j(\tilde{x} \mid t_j) f_j(\boldsymbol{x}\mid t_j)\pi_j(t_j)\,dt_j,\\
+ p(\tilde{x} \mid \boldsymbol{x}) &= \sum_{j} w_j \frac{1}{m_j(\boldsymbol{x})}\int_{\boldsymbol{\Theta}_j} f_j(\tilde{x} \mid t_j) f_j(\boldsymbol{x}\mid t_j)\pi_j(t_j)\,dt_j,\\
  \label{eq:predictive_1}
- &= \sum_{j} \pr(\mathcal{M}_j \mid \boldsymbol{x}) m_j(\tilde{x}).
+ &= \sum_{j} \pr(\mathcal{M}_j \mid \boldsymbol{x}) p_j(\tilde{x} \mid \boldsymbol{x}).
 \end{align}
 \end{frame}
 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%