Reorganized the folders and started a common script for the lectures.

bootstrap/code/bootstrapsem.m

@@ -0,0 +1,24 @@
+nsamples = 100;
+nresamples = 1000;
+
+% draw a SRS (simple random sample, "Stichprobe") from the population:
+x = randn( 1, nsamples );
+fprintf('%-30s  %-5s  %-5s  %-5s\n', '', 'mean', 'stdev', 'sem' )
+fprintf('%30s  %5.2f  %5.2f  %5.2f\n', 'single SRS', mean( x ), std( x ), std( x )/sqrt(nsamples) )
+
+% bootstrap the mean:
+mus = zeros(nresamples,1);  % vector for storing the means
+for i = 1:nresamples        % loop for generating the bootstraps
+    inx = randi(nsamples, 1, nsamples);  % range, 1D-vector, number
+    xr = x(inx);            % resample the original SRS
+    mus(i) = mean(xr);      % compute statistic of the resampled SRS
+end
+fprintf('%30s  %5.2f  %5.2f  -\n', 'bootstrapped distribution', mean( mus ), std( mus ) )
+
+% many SRS (we can do that with the random number generator, but not in real life!):
+musrs = zeros(nresamples,1);      % vector for the means of each SRS
+for i = 1:nresamples
+    x = randn( 1, nsamples );     % draw a new SRS
+    musrs(i) = mean( x );         % compute its mean
+end
+fprintf('%30s  %5.2f  %5.2f  -\n', 'sampling distribution', mean( musrs ), std( musrs ) )

bootstrap/lecture/Makefile

@@ -0,0 +1,22 @@
+BASENAME=bootstrap
+PYFILES=$(wildcard *.py)
+PYPDFFILES=$(PYFILES:.py=.pdf)
+
+pdf : $(BASENAME)-chapter.pdf $(PYPDFFILES)
+
+$(BASENAME)-chapter.pdf : $(BASENAME)-chapter.tex $(BASENAME).tex
+	pdflatex -interaction=scrollmode $< | tee /dev/stderr | fgrep -q "Rerun to get cross-references right" && pdflatex -interaction=scrollmode $< || true
+
+$(PYPDFFILES) : %.pdf : %.py
+	python $<
+
+clean :
+	rm -f *~ $(BASENAME)-chapter.aux $(BASENAME)-chapter.log $(BASENAME)-chapter.out $(BASENAME).aux $(BASENAME).log
+
+cleanall : clean
+	rm -f $(BASENAME)-chapter.pdf
+
+watch :
+	while true; do ! make -q pdf && make pdf; sleep 0.5; done
+
+

bootstrap/lecture/bootstrap-chapter.tex

@@ -0,0 +1,225 @@
+\documentclass[12pt]{report}
+
+%%%%% title %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+\title{\tr{Introduction to Scientific Computing}{Einf\"uhrung in die wissenschaftliche Datenverarbeitung}}
+\author{Jan Benda\\Abteilung Neuroethologie\\[2ex]\includegraphics[width=0.3\textwidth]{UT_WBMW_Rot_RGB}}
+\date{WS 15/16}
+
+%%%% language %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+% \newcommand{\tr}[2]{#1}  % en
+% \usepackage[english]{babel}
+\newcommand{\tr}[2]{#2}  % de
+\usepackage[german]{babel}
+
+%%%%% packages %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+\usepackage{pslatex}   % nice font for pdf file
+\usepackage[breaklinks=true,bookmarks=true,bookmarksopen=true,pdfpagemode=UseNone,pdfstartview=FitH,colorlinks=true,citecolor=blue]{hyperref}
+
+%%%% layout %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+\usepackage[left=25mm,right=25mm,top=20mm,bottom=30mm]{geometry}
+\setcounter{tocdepth}{1}
+
+%%%%% section style %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+\usepackage[sf,bf,it,big,clearempty]{titlesec}
+\setcounter{secnumdepth}{1}
+
+
+%%%%% units %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+\usepackage[mediumspace,mediumqspace,Gray]{SIunits}      % \ohm, \micro
+ 
+
+%%%%% figures %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+\usepackage{graphicx}
+\usepackage{xcolor}
+\pagecolor{white}
+
+\newcommand{\ruler}{\par\noindent\setlength{\unitlength}{1mm}\begin{picture}(0,6)%
+  \put(0,4){\line(1,0){170}}%
+  \multiput(0,2)(10,0){18}{\line(0,1){4}}%
+  \multiput(0,3)(1,0){170}{\line(0,1){2}}%
+  \put(0,0){\makebox(0,0){{\tiny 0}}}%
+  \put(10,0){\makebox(0,0){{\tiny 1}}}%
+  \put(20,0){\makebox(0,0){{\tiny 2}}}%
+  \put(30,0){\makebox(0,0){{\tiny 3}}}%
+  \put(40,0){\makebox(0,0){{\tiny 4}}}%
+  \put(50,0){\makebox(0,0){{\tiny 5}}}%
+  \put(60,0){\makebox(0,0){{\tiny 6}}}%
+  \put(70,0){\makebox(0,0){{\tiny 7}}}%
+  \put(80,0){\makebox(0,0){{\tiny 8}}}%
+  \put(90,0){\makebox(0,0){{\tiny 9}}}%
+  \put(100,0){\makebox(0,0){{\tiny 10}}}%
+  \put(110,0){\makebox(0,0){{\tiny 11}}}%
+  \put(120,0){\makebox(0,0){{\tiny 12}}}%
+  \put(130,0){\makebox(0,0){{\tiny 13}}}%
+  \put(140,0){\makebox(0,0){{\tiny 14}}}%
+  \put(150,0){\makebox(0,0){{\tiny 15}}}%
+  \put(160,0){\makebox(0,0){{\tiny 16}}}%
+  \put(170,0){\makebox(0,0){{\tiny 17}}}%
+  \end{picture}\par}
+
+% figures:
+\setlength{\fboxsep}{0pt}
+\newcommand{\texpicture}[1]{{\sffamily\footnotesize\input{#1.tex}}}
+%\newcommand{\texpicture}[1]{\fbox{\sffamily\footnotesize\input{#1.tex}}}
+%\newcommand{\texpicture}[1]{\setlength{\fboxsep}{2mm}\fbox{#1}}
+%\newcommand{\texpicture}[1]{}
+\newcommand{\figlabel}[1]{\textsf{\textbf{\large \uppercase{#1}}}}
+
+% maximum number of floats:
+\setcounter{topnumber}{2}
+\setcounter{bottomnumber}{0}
+\setcounter{totalnumber}{2}
+
+% float placement fractions:
+\renewcommand{\textfraction}{0.2}
+\renewcommand{\topfraction}{0.8}
+\renewcommand{\bottomfraction}{0.0}
+\renewcommand{\floatpagefraction}{0.5}
+
+% spacing for floats:
+\setlength{\floatsep}{12pt plus 2pt minus 2pt}
+\setlength{\textfloatsep}{20pt plus 4pt minus 2pt}
+\setlength{\intextsep}{12pt plus 2pt minus 2pt}
+
+% spacing for a floating page:
+\makeatletter
+  \setlength{\@fptop}{0pt}
+  \setlength{\@fpsep}{8pt plus 2.0fil}
+  \setlength{\@fpbot}{0pt plus 1.0fil}
+\makeatother
+
+% rules for floats:
+\newcommand{\topfigrule}{\vspace*{10pt}{\hrule height0.4pt}\vspace*{-10.4pt}}
+\newcommand{\bottomfigrule}{\vspace*{-10.4pt}{\hrule height0.4pt}\vspace*{10pt}}
+
+% captions:
+\usepackage[format=plain,singlelinecheck=off,labelfont=bf,font={small,sf}]{caption}
+
+% put caption on separate float:
+\newcommand{\breakfloat}{\end{figure}\begin{figure}[t]}
+
+% references to panels of a figure within the caption:
+\newcommand{\figitem}[1]{\textsf{\bfseries\uppercase{#1}}}
+% references to figures:
+\newcommand{\panel}[1]{\textsf{\uppercase{#1}}}
+\newcommand{\fref}[1]{\textup{\ref{#1}}}
+\newcommand{\subfref}[2]{\textup{\ref{#1}}\,\panel{#2}}
+% references to figures in normal text:
+\newcommand{\fig}{Fig.}
+\newcommand{\Fig}{Figure}
+\newcommand{\figs}{Figs.}
+\newcommand{\Figs}{Figures}
+\newcommand{\figref}[1]{\fig~\fref{#1}}
+\newcommand{\Figref}[1]{\Fig~\fref{#1}}
+\newcommand{\figsref}[1]{\figs~\fref{#1}}
+\newcommand{\Figsref}[1]{\Figs~\fref{#1}}
+\newcommand{\subfigref}[2]{\fig~\subfref{#1}{#2}}
+\newcommand{\Subfigref}[2]{\Fig~\subfref{#1}{#2}}
+\newcommand{\subfigsref}[2]{\figs~\subfref{#1}{#2}}
+\newcommand{\Subfigsref}[2]{\Figs~\subfref{#1}{#2}}
+% references to figures within bracketed text:
+\newcommand{\figb}{Fig.}
+\newcommand{\figsb}{Figs.}
+\newcommand{\figrefb}[1]{\figb~\fref{#1}}
+\newcommand{\figsrefb}[1]{\figsb~\fref{#1}}
+\newcommand{\subfigrefb}[2]{\figb~\subfref{#1}{#2}}
+\newcommand{\subfigsrefb}[2]{\figsb~\subfref{#1}{#2}}
+
+% references to tables:
+\newcommand{\tref}[1]{\textup{\ref{#1}}}
+% references to tables in normal text:
+\newcommand{\tab}{Tab.}
+\newcommand{\Tab}{Table}
+\newcommand{\tabs}{Tabs.}
+\newcommand{\Tabs}{Tables}
+\newcommand{\tabref}[1]{\tab~\tref{#1}}
+\newcommand{\Tabref}[1]{\Tab~\tref{#1}}
+\newcommand{\tabsref}[1]{\tabs~\tref{#1}}
+\newcommand{\Tabsref}[1]{\Tabs~\tref{#1}}
+% references to tables within bracketed text:
+\newcommand{\tabb}{Tab.}
+\newcommand{\tabsb}{Tab.}
+\newcommand{\tabrefb}[1]{\tabb~\tref{#1}}
+\newcommand{\tabsrefb}[1]{\tabsb~\tref{#1}}
+
+
+%%%%% equation references %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%\newcommand{\eqref}[1]{(\ref{#1})}
+\newcommand{\eqn}{\tr{Eq}{Gl}.}
+\newcommand{\Eqn}{\tr{Eq}{Gl}.}
+\newcommand{\eqns}{\tr{Eqs}{Gln}.}
+\newcommand{\Eqns}{\tr{Eqs}{Gln}.}
+\newcommand{\eqnref}[1]{\eqn~\eqref{#1}}
+\newcommand{\Eqnref}[1]{\Eqn~\eqref{#1}}
+\newcommand{\eqnsref}[1]{\eqns~\eqref{#1}}
+\newcommand{\Eqnsref}[1]{\Eqns~\eqref{#1}}
+
+
+%%%%% listings %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+\usepackage{listings}
+\lstset{
+  inputpath=../code,
+  basicstyle=\ttfamily\footnotesize,
+  numbers=left,
+  showstringspaces=false,
+  language=Matlab,
+  commentstyle=\itshape\color{darkgray},
+  keywordstyle=\color{blue},
+  stringstyle=\color{green},
+  backgroundcolor=\color{blue!10},
+  breaklines=true,
+  breakautoindent=true,
+  columns=flexible,
+  frame=single,
+  caption={\protect\filename@parse{\lstname}\protect\filename@base},
+  captionpos=t,
+  xleftmargin=1em,
+  xrightmargin=1em,
+  aboveskip=10pt
+}
+
+%%%%% math stuff: %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+\usepackage{amsmath}
+\usepackage{bm} 
+\usepackage{dsfont}
+\newcommand{\naZ}{\mathds{N}}
+\newcommand{\gaZ}{\mathds{Z}}
+\newcommand{\raZ}{\mathds{Q}}
+\newcommand{\reZ}{\mathds{R}}
+\newcommand{\reZp}{\mathds{R^+}}
+\newcommand{\reZpN}{\mathds{R^+_0}}
+\newcommand{\koZ}{\mathds{C}}
+
+
+%%%%% structure: %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+\usepackage{ifthen}
+
+\newcommand{\code}[1]{\texttt{#1}}
+
+\newcommand{\source}[1]{    
+  \begin{flushright}
+    \color{gray}\scriptsize \url{#1}
+  \end{flushright}
+}
+
+\newenvironment{definition}[1][]{\medskip\noindent\textbf{Definition}\ifthenelse{\equal{#1}{}}{}{ #1}:\newline}%
+  {\medskip}
+
+\newcounter{maxexercise} 
+\setcounter{maxexercise}{9}  % show listings up to exercise maxexercise
+\newcounter{theexercise} 
+\setcounter{theexercise}{1}
+\newenvironment{exercise}[1][]{\medskip\noindent\textbf{\tr{Exercise}{\"Ubung}
+  \arabic{theexercise}:}\newline \newcommand{\exercisesource}{#1}}%
+  {\ifthenelse{\equal{\exercisesource}{}}{}{\ifthenelse{\value{theexercise}>\value{maxexercise}}{}{\medskip\lstinputlisting{\exercisesource}}}\medskip\stepcounter{theexercise}}
+
+\graphicspath{{figures/}}
+
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+\begin{document} 
+
+\include{bootstrap}
+
+\end{document}

bootstrap/lecture/bootstrap.tex

@@ -0,0 +1,64 @@
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+\chapter{\tr{Bootstrap Methods}{Bootstrap Methoden}}
+
+Beim Bootstrap erzeugt man sich die Verteilung von Statistiken durch Resampling
+aus der Stichprobe. Das hat mehrere Vorteile:
+\begin{itemize}
+\item Weniger Annahmen (z.B. muss eine Stichprobe nicht Normalverteilt sein).
+\item H\"ohere Genauigkeit als klassische Methoden.
+\item Allgemeing\"ultigkeit: Bootstrap Methoden sind sich sehr
+  \"ahnlich f\"ur viele verschiedene Statistiken und ben\"otigen nicht
+  f\"ur jede Statistik eine andere Formel.
+\end{itemize}
+
+\begin{figure}[t]
+  \includegraphics[width=0.8\textwidth]{2012-10-29_16-26-05_771}\\[2ex]
+  \includegraphics[width=0.8\textwidth]{2012-10-29_16-41-39_523}\\[2ex]
+  \includegraphics[width=0.8\textwidth]{2012-10-29_16-29-35_312}
+  \caption{\tr{Why can we only measure a sample of the
+      population?}{Warum k\"onnen wir nur eine Stichprobe der
+      Grundgesamtheit messen?}}
+\end{figure}
+
+\begin{figure}[t]
+  \includegraphics[height=0.2\textheight]{srs1}\\[2ex]
+  \includegraphics[height=0.2\textheight]{srs2}\\[2ex]
+  \includegraphics[height=0.2\textheight]{srs3}
+  \caption{Bootstrap der Stichprobenvertielung (a) Von der
+    Grundgesamtheit (population) mit unbekanntem Parameter
+    (z.B. Mittelwert $\mu$) zieht man Stichproben (SRS: simple random
+    samples).  Die Statistik (hier Bestimmung von $\bar x$) kann f\"ur
+    jede Stichprobe berechnet werden. Die erhaltenen Werte entstammen
+    der Stichprobenverteilung. Meisten wird aber nur eine Stichprobe
+    gezogen!  (b) Mit bestimmten Annahmen und Theorien kann man auf
+    die Stichprobenverteilung schlie{\ss}en ohne sie gemessen zu
+    haben.  (c) Alternativ k\"onnen aus der einen Stichprobe viele
+    Bootstrap-Stichproben generiert werden (resampling) und so
+    Eigenschaften der Stichprobenverteilung empirisch bestimmt
+    werden. Aus Hesterberg et al. 2003, Bootstrap Methods and
+    Permuation Tests}
+\end{figure}
+
+\section{Bootstrap des Standardfehlers}
+
+Beim Bootstrap erzeugen wir durch Resampling neue Stichproben und
+benutzen diese um die Stichprobenverteilung einer Statistik zu
+berechnen. Die Bootstrap Stichproben haben jeweils den gleichen Umfang
+wie die urspr\"unglich gemessene Stichprobe und werden durch Ziehen
+mit Zur\"ucklegen gewonnen. Jeder Wert der urspr\"unglichen Stichprobe
+kann also einmal, mehrmals oder gar nicht in einer Bootstrap
+Stichprobe vorkommen.
+
+\begin{exercise}[bootstrapsem.m]
+  Ziehe 1000 normalverteilte Zufallszahlen und berechne deren Mittelwert,
+  Standardabweichung und Standardfehler ($\sigma/\sqrt{n}$).
+
+  Resample die Daten 1000 mal (Ziehen mit Zur\"ucklegen) und berechne jeweils
+  den Mittelwert.
+
+  Plotte ein Histogramm dieser Mittelwerte, sowie deren Mittelwert und
+  die Standardabweichung.
+
+  Was hat das mit dem Standardfehler zu tun?
+\end{exercise}