[lecture] Updates (#479)

* Tom's June 23 edits of two Wald lectures and rearranging order of lectures

* updates

* updates

* updates

* updates

* updates

* update code

* updates

* updates

* minor update

* Tom's June 25 edits of first Wald-Friedman lecture

* updates

* updates

* update

* minor updates

* updates

* updates

* Tom's June 26 first edits of two Wald lectures

* Tom's June 30 edits of two Wald lectures

* Tom's July 1 edits of two Wald lectures

* Update lectures/wald_friedman.md

* Update lectures/wald_friedman.md

* Update lectures/wald_friedman.md

* Update lectures/wald_friedman.md

* update lecrture

* updates

* update according to John's suggestions

* minor update

* syntax updates

---------

Co-authored-by: thomassargent30 <ts43@nyu.edu>
Co-authored-by: Humphrey Yang <u6474961@anu.edu.au>

Author: 3 people

lectures/_static/lecture_specific/wald_friedman/wald_dec_rule.pdf

@@ -17,20 +17,16 @@
     \draw[thick] (0, 0)  -- (3, 0) node[below] {};
     %curly bracket
     \draw [decorate, very thick] (s0) -- (s1)
-        node [midway, anchor=south,  outer sep=10pt]{accept $f_1$};
+        node [midway, anchor=south,  outer sep=10pt]{accept $f_0$};
     \draw [decorate, very thick] (s1) -- (s2)
         node [midway, anchor=south, outer sep=10pt]{draw again};
     \draw [decorate, very thick] (s2) -- (s3)
-        node [midway, anchor=south, outer sep=10pt]{accept $f_0$};
-    \node[circle, draw, thin, blue, fill=white!10, scale=0.45] at (a0){};
-    \node[below, outer sep=5pt] at (a0){$0$};
+        node [midway, anchor=south, outer sep=10pt]{accept $f_1$};
     \node[circle, draw, thin, blue, fill=white!10, scale=0.45] at (a1){};
-    \node[below, outer sep=5pt] at (a1){$\beta$};
+    \node[below, outer sep=5pt] at (a1){$B$};
     \node[circle, draw, thin, blue, fill=white!10, scale=0.45] at (a2){};
-    \node[below, outer sep=5pt] at (a2){$\alpha$};
-    \node[circle, draw, thin, blue, fill=white!10, scale=0.45] at (a3){};
-    \node[below, outer sep=5pt] at (a3){$1$};
-    \node[below, outer sep=25pt] at (1.5, 0){values of $\pi$};
+    \node[below, outer sep=5pt] at (a2){$A$};
+    \node[below, outer sep=25pt] at (1.5, 0){value of $L_m$};
 \end{tikzpicture}
 
 \end{document}

lectures/_static/lecture_specific/wald_friedman/wald_dec_rule.png

@@ -0,0 +1,36 @@
+\documentclass[convert={density=300,size=1080x800,outext=.png}]{standalone}
+\usepackage{tikz}
+\usetikzlibrary{decorations.pathreplacing}
+\begin{document}
+
+%.. tikz:: 
+\begin{tikzpicture}
+[scale=5, every node/.style={color=black}, decoration={brace,amplitude=7pt}] \coordinate (a0) at (0, 0.0);
+    \coordinate (a1) at (1, 0.0);
+    \coordinate (a2) at (2, 0.0);
+    \coordinate (a3) at (3, 0.0);
+    \coordinate (s0) at (0, 0.1);
+    \coordinate (s1) at (1, 0.1);
+    \coordinate (s2) at (2, 0.1);
+    \coordinate (s3) at (3, 0.1);
+    % axis
+    \draw[thick] (0, 0)  -- (3, 0) node[below] {};
+    %curly bracket
+    \draw [decorate, very thick] (s0) -- (s1)
+        node [midway, anchor=south,  outer sep=10pt]{accept $f_0$};
+    \draw [decorate, very thick] (s1) -- (s2)
+        node [midway, anchor=south, outer sep=10pt]{draw again};
+    \draw [decorate, very thick] (s2) -- (s3)
+        node [midway, anchor=south, outer sep=10pt]{accept $f_1$};
+        \node[circle, draw, thin, blue, fill=white!10, scale=0.45] at (a0){};
+        \node[below, outer sep=5pt] at (a0){$0$};
+        \node[circle, draw, thin, blue, fill=white!10, scale=0.45] at (a1){};
+        \node[below, outer sep=5pt] at (a1){$B$};
+        \node[circle, draw, thin, blue, fill=white!10, scale=0.45] at (a2){};
+        \node[below, outer sep=5pt] at (a2){$A$};
+        \node[circle, draw, thin, blue, fill=white!10, scale=0.45] at (a3){};
+        \node[below, outer sep=5pt] at (a3){$1$};
+    \node[below, outer sep=25pt] at (1.5, 0){values of $\pi$};
+\end{tikzpicture}
+
+\end{document}

lectures/_static/lecture_specific/wald_friedman/wald_dec_rule.tex

@@ -2568,4 +2568,11 @@ @article{hall1971dynamic
   pages={229--244},
   year={1971},
   publisher={Wiley-Blackwell}
-}
+}
+
+@article{fischer2024improving,
+  title={Improving the (approximate) sequential probability ratio test by avoiding overshoot},
+  author={Fischer, Lasse and Ramdas, Aaditya},
+  journal={arXiv preprint arXiv:2410.16076},
+  year={2024}
+}

lectures/_static/lecture_specific/wald_friedman_2/wald_dec_rule.pdf

@@ -23,6 +23,23 @@ parts:
   - file: back_prop
   - file: rand_resp
   - file: util_rand_resp
+- caption: Bayes Law
+  numbered: true
+  chapters:
+  - file:  bayes_nonconj
+  - file:  ar1_bayes
+  - file:  ar1_turningpts
+- caption: Statistics and Information 
+  numbered: true
+  chapters:
+  - file: likelihood_ratio_process
+  - file: imp_sample
+  - file: wald_friedman
+  - file: wald_friedman_2
+  - file: exchangeable
+  - file: likelihood_bayes
+  - file: mix_model
+  - file: navy_captain
 - caption: Linear Programming
   numbered: true
   chapters:
@@ -49,6 +66,7 @@ parts:
   - file: career
   - file: jv
   - file: mccall_q
+  - file: odu
 - caption: Consumption, Savings and Capital
   numbered: true
   chapters:
@@ -64,25 +82,6 @@ parts:
   - file: egm_policy_iter
   - file: ifp
   - file: ifp_advanced
-
-- caption: Bayes Law
-  numbered: true
-  chapters:
-  - file:  bayes_nonconj
-  - file:  ar1_bayes
-  - file:  ar1_turningpts
-
-- caption: Information
-  numbered: true
-  chapters:
-  - file: odu
-  - file: likelihood_ratio_process
-  - file: imp_sample
-  - file: wald_friedman
-  - file: exchangeable
-  - file: likelihood_bayes
-  - file: mix_model
-  - file: navy_captain
 - caption: LQ Control
   numbered: true
   chapters:

lectures/_static/lecture_specific/wald_friedman_2/wald_dec_rule.png

@@ -544,6 +544,7 @@ control tests during World War II.
 A Navy Captain who had been ordered to perform tests of this kind had doubts about it that he
 presented to Milton Friedman, as we describe in  {doc}`this lecture <wald_friedman>`.
 
+(rel_entropy)=
 ## Kullback–Leibler Divergence
 
 Now let’s consider a case in which neither $g$ nor $f$