Merge branch 'master' of code.communitydata.science:cdsc_examples_repository into master

knitr_examples/latex_homework_assignment/HW1.Rnw

@@ -0,0 +1,228 @@
+% based on mako's mod
+\documentclass[12pt]{memoir}
+
+% based on kieran healy's memoir modifications
+\usepackage{mako-mem}
+\chapterstyle{article-3}
+\pagestyle{memo}
+\usepackage{wrapfig}
+\usepackage{ucs}
+\usepackage[utf8x]{inputenc}
+
+<<init, echo=FALSE>>=
+knit_hooks$set(document = function(x) {
+  sub('\\usepackage[]{color}',
+'\\usepackage[usenames,dvipsnames]{color}', x, fixed = TRUE)
+})
+
+bold <- function(x) {paste('{\\textbf{',x,'}}', sep ='')}
+gray <- function(x) {paste('{\\textcolor{gray}{',x,'}}', sep ='')}
+wrapify <- function (x) {paste("{", x, "}", sep="")}
+
+load("knitr_data.RData")
+attach(r)
+f <- function (x) {formatC(x, format="d", big.mark=',')}
+format.percent <- function(x) {paste(f(x*100),"\\%",sep='')}
+format.day.ordinal <- function(x) {
+    day <- format(x,format="%d")
+    daylast <- substr(day,nchar(day),nchar(day))
+    dayfirst <- substr(day,1,1)
+    if(dayfirst == '0')
+        day = daylast
+
+    if( daylast == "1")
+        day <- paste0(day,"st")
+    else if(daylast == "2")
+        day <- paste0(day,"nd")
+    else if (daylast == "3")
+        day <- paste0(day,"rd")
+    else
+        day <- paste0(day,"th")
+        
+    return(day)
+}
+format.month <- function(x){
+    return( format(x,format='%B %Y'))
+}
+format.date <- function(x)
+{
+    return(paste(format(x,format = '%B'),format.day.ordinal(x),format(x,format='%Y'),sep=' '))
+}
+@
+
+\usepackage[T1]{fontenc}
+\usepackage{textcomp}
+\usepackage[garamond]{mathdesign}
+
+\usepackage[letterpaper,left=1.65in,right=1.65in,top=1.3in,bottom=1.2in]{geometry}
+
+% packages i use in essentially every document
+\usepackage{graphicx}
+\newsubfloat{figure}
+\usepackage{enumerate}
+
+% packages i use in many documents but leave off by default
+\usepackage{amsmath, amsthm, amssymb}
+% \usepackage{dcolumn}
+% \usepackage{endfloat}
+
+% import and customize urls
+\usepackage[breaklinks]{hyperref}
+\hypersetup{colorlinks=true, linkcolor=Black, citecolor=Black, filecolor=Blue,
+    urlcolor=Blue, unicode=true}
+
+% add bibliographic stuff 
+\usepackage[round]{natbib}
+\def\citepos#1{\citeauthor{#1}'s (\citeyear{#1})}
+\def\citespos#1{\citeauthor{#1}' (\citeyear{#1})}
+
+% memoir function to take out of the space out of the whitespace lists
+\firmlists
+
+\everymath{\displaymode}
+\begin{document}
+
+\setlength{\parskip}{4.5pt}
+\baselineskip 16pt
+
+\title{STAT 544 HW1}
+\author{Nathan TeBlunthuis\\
+        \href{mailto:nathante@uw.edu}{nathante@uw.edu}}
+
+\maketitle
+
+\subsubsection{1.a}
+\[u^{STOP}(s) = 
+  \begin{cases}
+    s & \quad s <= S  \\
+    0 & \quad \mathrm{otherwise}
+  \end{cases}
+\]
+This is given in the problem statement.
+
+  \subsubsection{1.b}
+\newcommand{\ugoon}[1]{\overline{u}^{*GO~ON}(#1)}
+\newcommand{\ubarstar}[1]{\overline{u}^*(#1)}
+\newcommand{\ustop}[1]{u^{STOP}(#1)}
+\newcommand{\ustareq}[1]{max \left \{\ugoon{#1}, \ustop{#1} \right\}}
+\[
+  u^*(s) = \ustareq{s}
+\]
+\[
+  \ugoon{s} = \sum_{x = 1}^{R}{\ubarstar{s+x}p(x)} = \frac{1}{R}\sum_{x=1}^{R}\ubarstar{s+x}
+\]
+\[\ugoon{S} = \frac{1}{R}\sum_{x=1}^{R}\ubarstar{S+x} = \frac{1}{R}\sum_{x=1}^R0 = 0\]
+
+Since \(S + x > S\) and \(u(s) = 0\) for all \(s > S\).
+
+Therefore \[\ubarstar{S} = \ustareq{S} = max\left\{0,S\right\} = S\]
+
+\subsubsection{1.c}
+Code below:
+<<<1.c,echo=TRUE, fig.height=4,fig.width=6,fig.cap="The expected utility of following the optimal strategy is stricly greater than the value of stopping until it is possible that \\(S < s\\) after the next roll. The expected utility is greater when the odds of having an additional safe roll are greater." >>=
+R <- 6;
+S <- 20;
+
+# use memoization to speed up dynamic programming
+u.star <- function(s){
+    memo <<- array(dim=S+R)
+    u.star.step(s)
+}
+
+u.star.step <- function(s){
+    if(is.na(memo[[s+1]])){
+        memo[[s+1]] <<- u.star.comp(s)
+    }
+    memo[[s+1]]
+}
+
+u.star.comp <- function(s){
+    if (s > S) return(0);
+    if (s == S) return(s);
+    go.on <- sum(sapply(1:R,function(x) u.star.step(s+x)))/R;
+    max(s, go.on)
+}
+
+library(ggplot2)
+df <- data.frame(x=0:S,y=sapply(0:S,u.star))
+p <- ggplot(df,aes(x=x,y=y)) 
+p <- p + geom_line(aes(linetype='max expected')) 
+p <- p + geom_point() 
+p <- p + scale_y_continuous('utility',limits=c(0,S))
+p <- p + scale_x_continuous('s') + theme_minimal()  
+p <- p + geom_abline(aes(linetype='always stop', slope=1,intercept=0))
+p <- p + scale_linetype_manual(name='',values=c("always stop"='dashed',
+                                                "max expected"='solid'))
+print(p)
+@
+
+\clearpage
+
+\subsubsection{1.d}
+
+\newcommand{\sumxr}[1]{\frac{1}{R}\sum_{x=1}^R{#1}}
+\newcommand{\sumxrest}[1]{\frac{1}{R}\sum_{x=1}^{R - (S -s)}{#1}}
+  
+\[\mathrm{Let}~ s < S - R ~\mathrm{then}~ s + x \le S ~\mathrm{for}~ x \in \{1,...R\}. \]
+
+\[\mathrm{So}~ \ubarstar{s+x} = \mathrm{max}\{s + x, \sumxr{\ubarstar{s + x}}\}\]
+
+\[\mathrm{Since~we~know}~  \(s + x > s\), \(\ubarstar{s} = \sumxr{\ubarstar{s+x}} = \ugoon{s}\]. 
+
+\[\mathrm{So~if}~ \(s < S - R\), \(\pi^*(s) = GO~ON\].
+
+We can see that \(\ubarstar{s} \ge s\) since our decisions are \(GO~ON\) which implies that \(\ubarstar{s} \ge u^{STOP}(s)\) and \(STOP\) which yields \(\ubarstar{s}={s}\). 
+
+\subsubsection{2.a}
+\newcommand{\piof}[1]{_{\pi({#1})}}
+\newcommand{\pistarof}[1]{_{\pi^*({#1})}}
+
+Prove that if \(X_1,...X_n\) is \mathit{n}-exchangeable, then \(X_1,...X_m\) is m-exchangeable for any \(m < n\). 
+
+\[P(X_1,...X_n) = P(X\piof{1},...X\piof{2}) ~\mbox{for all}~ \pi \in \mathbb{S}_n\]
+
+Choose a permutation \[\pi \in \mathbb{S}_n ~\mbox{such that for all}~ i > m ~\mbox{,}~ \pi(i) = i\]. Then \[P(X\piof{1},...X\piof{m} | X\piof{m+1},...X\piof{n}) = P(X\piof{1},...X\piof{m} | X_{m+1},...X_n) = \frac{P(X\piof{1},...X\piof{m})}{P(X_{m+1},...X_n)}\]. 
+
+And, since  \(X_1,...X_n\) is exchangeable, \[P(X\piof{1},...X\piof{m} | X\piof{m+1},...X\piof{n}) = P(X_1,...X_m | X_{m+1},...X_n) \quad = \quad \frac{P(X_1,...X_m)}{P(X_{m+1},...X_n)}\] 
+Therefore 
+\[ P(X_1,...X_m) =  P(X\piof{1},...X\piof{m})\]
+
+Which means that \(X_{1},...X_{m}\) is exchangeable.
+\subsubsection{2.b}
+
+To show that if \(X_{1},...X_{n}\) is exchangeable, then \(P(X_1) = P(X_m)\) for all \(m \le n\), \[\mbox{choose a permutation}~\pi\) ~\mbox{such that}~ \pi_1 = 1,~ \pi_2 = m\] 
+
+\[\mbox{Note that}~X\piof{1},...X\piof{n}~\mbox{is exchangeable. Therefore}~ X\piof{1},X\piof{2} \mbox{is exchangeable, by 2.a.} \] 
+
+So we have \[P(X_1,X_m) = P(X_m,X_1) \rightarrow P(X_1|X_m) = P(X_m|X_1) \rightarrow \frac{P(X_1)}{P(X_m)}=\frac{P(X_m)}{P(X_1)}}\]
+\[\rightarrow P(X_1)P(X_1)=P(X_m)P(X_m) \] 
+So since \(P(X_1),P(X_m)>0\), \[P(X_1) = P(X_m)\] 
+
+\subsubsection{2.c}
+\newcommand{\sn}{X_1+...X_n}
+\newcommand{\sN}{X_1+...X_N}
+\newcommand{\spin}{X_{\pi(1)}+...X_{\pi(n)}}
+\newcommand{\sumn}[1]{\sum_{N_1=n_1}^{n_1+N-n}{#1}}
+\newcommand{\crhs}{\sumn{P[X_1+ ... X_N = N_1] {N_1 \choose n_1} {N-N_1 \choose n-n_1} / {N \choose n}}}
+
+To show that \[P[\sn=n_1]=\crhs\]
+
+See that there are \(n \choose n_1\) ways that \(\sn=n_1\).
+
+By exchangeability, for any permutation \(\pi\) of \(N\) such that \(\spin=n_1\). 
+
+\[P(\sn=n_1)=\({n \choose n_1}\)p(\spin)\]
+
+The number of permutations \(\pi\) of \(N\) such that \(\spin=n_1\) depends on \(\sN\). We know \(\sN \ge n_1\) otherwise \(\sn < \sN\). Also \(\sN  \le n_1+ N - n\) since if \(\sN > n_1 + N - n \) then \(N - (\sN) \le n - n_1\) which would mean that there are more zeros in the sequence \(X_1,...X_n\) than in the sequence \(X_1,...X_N\). 
+Therefore 
+
+\[P(\sn=n_1) =  \sumn{P(\sn=n_1 | \sN=N_1)P(\sN=N_1)}\]
+
+There \(N \choose n\) ways to pick a permutation of N giving the sequence \(X_1,...X_n\). Of these, there are  \(N_1 \choose n_1\) ways of choosing the 1's and \({N-N_1 \choose n-n_1}\) ways of choosing the 0s such that \(\sn=n_1\). Therefore 
+\[P(\sn=n_1 | \sN=N_1) =  {N_1 \choose n_1} {N-N_1 \choose n-n_1}  / {N \choose n}\]
+
+and we have  \[P[\sn=n_1]=\crhs\].
+
+\end{document}
+
+

knitr_examples/latex_homework_assignment/HW1Code.R

@@ -0,0 +1,34 @@
+R <- 6;
+S <- 20;
+
+# use memoization to speed up dynamic programming
+u.star <- function(s){
+    memo <<- array(dim=S+R)
+    u.star.step(s)
+}
+
+u.star.step <- function(s){
+    if(is.na(memo[[s+1]])){
+        memo[[s+1]] <<- u.star.comp(s)
+    }
+    memo[[s+1]]
+}
+
+u.star.comp <- function(s){
+    if (s > S) return(0);
+    if (s == S) return(s);
+    go.on <- sum(sapply(1:R,function(x) u.star.step(s+x)))/R;
+    max(s, go.on)
+}
+
+library(ggplot2)
+df <- data.frame(x=0:S,y=sapply(0:S,u.star))
+p <- ggplot(df,aes(x=x,y=y)) 
+p <- p + geom_line(aes(linetype='max expected')) 
+p <- p + geom_point() 
+p <- p + scale_y_continuous('utility',limits=c(0,S))
+p <- p + scale_x_continuous('s') + theme_minimal()  
+p <- p + geom_abline(aes(linetype='always stop', slope=1,intercept=0))
+p <- p + scale_linetype_manual(name='',values=c("always stop"='dashed',
+                                                "max expected"='solid'))
+print(p)

knitr_examples/latex_homework_assignment/Makefile

@@ -0,0 +1,31 @@
+#!/usr/bin/make
+
+all: $(patsubst %.Rnw,%.pdf,$(wildcard *.Rnw)) 
+pdf: all
+
+refs-processed.bib: 
+	perl -p -e 's/©//' refs.bib > refs-processed.bib
+	perl -0pe 's/,\s+(file|abstract|note) = \{.*?\}(,\n|\n)/\2/sg' refs-processed.bib |sponge refs-processed.bib
+	recode -d u8..ltex < refs-processed.bib | sponge refs-processed.bib
+
+%.tex: %.Rnw
+	Rscript -e "library(knitr); knit('$<')"
+
+%.pdf: %.tex refs-processed.bib
+	latexmk -f -pdf -quiet $<
+
+clean: 
+	latexmk -f -pdf -quiet -c *.tex
+	rm -f *.tex
+	rm -f *.tmp
+	rm -f vc
+	rm -f refs-processed.bib
+
+viewpdf: all
+	evince *.pdf
+
+spell:
+	aspell -c -t --tex-check-comments -b text.tex
+
+.PHONY: clean all
+.PRECIOUS: %.tex all

knitr_examples/latex_homework_assignment/mako-mem.sty

@@ -0,0 +1,232 @@
+% Some article styles and page layout tweaks for the LaTeX Memoir class.
+%
+% Copyright 2009 Benjamin Mako Hill <mako@atdot.cc>
+% Copyright 2008-2009 Kieran Healy <kjhealy@soc.duke.edu>
+
+% Distributed as free software under the GNU GPL v3
+
+% This file is heavily based on one by Kieran Healy
+% available here: http://github.com/kjhealy/latex-custom-kjh/
+
+\usepackage{lastpage}
+
+% blank footnote
+% Use \symbolfootnote[0]{Footnote text} for a blank footnote. 
+% Useful for initial acknowledgment note.
+\long\def\symbolfootnote[#1]#2{\begingroup%
+\def\thefootnote{\fnsymbol{footnote}}\footnote[#1]{#2}\endgroup}
+
+% put a period after the section numbers
+\setsecnumformat{\csname the#1\endcsname.\enspace}
+
+% >> article-1 << 
+\makechapterstyle{article-1}{
+ \renewcommand{\rmdefault}{ugm}
+ \renewcommand{\sfdefault}{phv}
+
+ \setsecheadstyle{\large\scshape}
+ \setsubsecheadstyle{\normalsize\itshape}
+ \renewcommand{\printchaptername}{}
+ \renewcommand{\chapternamenum}{}
+ \renewcommand{\chapnumfont}{\chaptitlefont}
+ \renewcommand{\printchapternum}{\chapnumfont \thechapter\space}
+ \renewcommand{\afterchapternum}{}
+ \renewcommand{\printchaptername}{\secheadstyle}
+ \renewcommand{\cftchapterfont}{\normalfont}
+ \renewcommand{\cftchapterpagefont}{\normalfont\scshape}
+ \renewcommand{\cftchapterpresnum}{\scshape}
+ \captiontitlefont{\small}
+ 
+ % turn off chapter numbering
+ \counterwithout{section}{chapter}
+ \counterwithout{figure}{chapter}
+ \counterwithout{table}{chapter}
+ 
+ % reduce skip after section heading
+ \setaftersecskip{1.2ex}
+ 
+ \pretitle{\newline\centering \LARGE\scshape \MakeLowercase }
+ \posttitle{\par\vskip 1em}
+ \predate{\footnotesize \centering}
+ \postdate{\par\vskip 1em}
+ 
+ % 'abstract' title, bigger skip from title
+ \renewcommand{\abstractname}{}
+ \abstractrunin
+
+% set name of bibliography to 'references'
+\renewcommand{\bibname}{References}
+}
+
+% >> article-2 <<
+\makechapterstyle{article-2}{
+ \renewcommand{\rmdefault}{ugm}
+ \renewcommand{\sfdefault}{phv}
+
+ \setsecheadstyle{\large\scshape} 
+ \setsubsecheadstyle{\normalsize\itshape} 
+ \setaftersubsubsecskip{-1em}
+ \setsubsubsecheadstyle{\bfseries}
+ \renewcommand{\printchaptername}{} 
+ \renewcommand{\chapternamenum}{} 
+ \renewcommand{\chapnumfont}{\chaptitlefont} 
+ \renewcommand{\printchapternum}{\chapnumfont \thechapter\space} 
+ \renewcommand{\afterchapternum}{} 
+ \renewcommand{\printchaptername}{\secheadstyle}
+ \renewcommand{\cftchapterfont}{\normalfont} 
+ \renewcommand{\cftchapterpagefont}{\normalfont\scshape} 
+ \renewcommand{\cftchapterpresnum}{\scshape} 
+ \captiontitlefont{\small}
+ 
+ % turn off chapter numbering
+ \counterwithout{section}{chapter}
+ \counterwithout{figure}{chapter}
+ \counterwithout{table}{chapter}
+ 
+ % supress chapter numbers 
+ \maxsecnumdepth{chapter} 
+ \setsecnumdepth{chapter}
+ 
+ % for numbered sections and subsections:
+ % (a) comment out the above stanza; (b) uncomment the one below
+ % \maxsecnumdepth{subsection} 
+ % \setsecnumdepth{subsection}
+
+ % reduce skip after section heading
+ \setaftersecskip{1.7ex}
+ 
+ % Title flush left
+ \pretitle{\flushleft\LARGE \itshape}
+ \posttitle{\par\vskip 0.5em}
+ \preauthor{\flushleft  \large \lineskip 1em}
+ \postauthor{\par\lineskip 1em}
+ \predate{\flushleft\footnotesize\vspace{0.65em}}
+ \postdate{\par\vskip 1em}
+ 
+ % 'abstract' title, bigger skip from title
+ \renewcommand{\abstractname}{Abstract:}
+ \renewcommand{\abstractnamefont}{\normalfont\small\bfseries}
+ \renewcommand{\abstracttextfont}{\normalfont\small}
+ \setlength{\absparindent}{0em}
+ \setlength{\abstitleskip}{-1.5em}
+ \abstractrunin
+
+ % set name of bibliography to 'references'
+ \renewcommand{\bibname}{References}
+}
+
+
+% >> article-3 <<
+\makechapterstyle{article-3}{
+ \renewcommand{\rmdefault}{ugm}
+ \renewcommand{\sfdefault}{phv}
+
+ \setsecheadstyle{\large\sffamily\bfseries\MakeUppercase} 
+ \setsubsecheadstyle{\normalsize\itshape} 
+ \setaftersubsubsecskip{-1em}
+ \setsubsubsecheadstyle{\small\bfseries}
+ \renewcommand{\printchaptername}{} 
+ \renewcommand{\chapternamenum}{} 
+ \renewcommand{\chapnumfont}{\chaptitlefont} 
+ \renewcommand{\printchapternum}{\chapnumfont \thechapter\space} 
+ \renewcommand{\afterchapternum}{} 
+ \renewcommand{\printchaptername}{\secheadstyle}
+ \renewcommand{\cftchapterfont}{\normalfont} 
+ \renewcommand{\cftchapterpagefont}{\normalfont\scshape} 
+ \renewcommand{\cftchapterpresnum}{\scshape} 
+ \captiontitlefont{\small}
+
+ % turn off chapter numbering
+ \counterwithout{section}{chapter}
+ \counterwithout{figure}{chapter}
+ \counterwithout{table}{chapter}
+ 
+ % supress chapter numbers 
+ \maxsecnumdepth{chapter} 
+ \setsecnumdepth{chapter}
+
+ % reduce skip after section heading
+ \setaftersecskip{1pt}
+ \setbeforesecskip{-1em}
+ 
+ % 'abstract' title, bigger skip from title
+ % \renewcommand{\maketitle}{\{\preauthor \theauthor\} \hfill \thetitle}
+ \renewcommand{\maketitle}{
+    {\Large\sffamily\bfseries\MakeUppercase\thetitle} \hfill
+    {\Large\sffamily\MakeUppercase\theauthor}
+    \vskip 0.7em}
+ \renewcommand{\abstractname}{\normalfont\scriptsize\noindent}
+ \renewcommand{\abstracttextfont}{\normalfont\scriptsize}
+ \abstractrunin
+
+ % set name of bibliography to 'references'
+ \renewcommand{\bibname}{References}
+
+ \parindent 0pt
+
+}
+
+%%% Custom styles for headers and footers
+%%% Basic 
+\makepagestyle{mako-mem}
+%\makeevenfoot{mako-mem}{\thepage}{}{}
+%\makeoddfoot{mako-mem}{}{}{\thepage}
+%\makeheadrule{mako-mem}{\textwidth}{\normalrulethickness}
+\newcommand{\@makomarks}{%
+  \let\@mkboth\markboth
+  \def\chaptermark##1{%
+    \markboth{%
+      \ifnum \c@secnumdepth >\m@ne
+        \if@mainmatter
+          \thechapter. \ %
+        \fi
+      \fi
+      ##1}{}}
+  \def\sectionmark##1{%
+    \markright{##1}}
+}
+\makepsmarks{mako-mem}{\@makomarks}
+\makepsmarks{mako-mem}{}
+\makeevenhead{mako-mem}{}{}{\scshape\thepage}
+\makeoddhead{mako-mem}{}{}{\scshape\thepage}
+
+%%% version control info in footers; requires vc package 
+% Make the style for vc-git revision control headers and footers
+\makepagestyle{mako-mem-git}
+\newcommand{\@gitmarks}{%
+  \let\@mkboth\markboth
+  \def\chaptermark##1{%
+    \markboth{%
+      \ifnum \c@secnumdepth >\m@ne
+        \if@mainmatter
+          \thechapter. \ %
+        \fi
+      \fi
+      ##1}{}}
+  \def\sectionmark##1{%
+    \markright{##1}}
+}
+\makepsmarks{mako-mem-git}{\@gitmarks}
+\makeevenhead{mako-mem-git}{}{}{\scshape\thepage}
+\makeoddhead{mako-mem-git}{}{}{\scshape\thepage}
+\makeevenfoot{mako-mem-git}{}{\texttt{\footnotesize{\textcolor{Blue}{git revision \VCRevision\ on \VCDateTEX}}}}{}
+\makeoddfoot{mako-mem-git}{}{\texttt{\footnotesize \textcolor{Blue}{git revision \VCRevision\ on \VCDateTEX}}}{}
+
+%% Create a command to make a note at the top of the first page describing the
+%% publication status of the paper. 
+\newcommand{\published}[1]{% 
+   \gdef\puB{#1}} 
+   \newcommand{\puB}{} 
+   \renewcommand{\maketitlehooka}{% 
+       \par\noindent\footnotesize \puB} 
+
+\makepagestyle{memo}
+\makeevenhead{memo}{}{}{}
+\makeoddhead{memo}{}{}{}
+
+\makeevenfoot{memo}{}{\scshape \thepage/\pageref{LastPage}}{}
+\makeoddfoot{memo}{}{\scshape \thepage/\pageref{LastPage}}{}
+
+
+\endinput
+