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Updated maximum likelihood chapter.

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Common latex header file.
This commit is contained in:
Jan Benda
2015-10-31 20:45:32 +01:00
parent 91f1f3663e
commit 40a5343fa8
20 changed files with 429 additions and 1452 deletions
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2
statistics/lecture/pdfprobabilities.py
View File

@@ -8,7 +8,7 @@ x1=0.0
x2=1.0
plt.xkcd()
fig = plt.figure( figsize=(6,4) )
fig = plt.figure( figsize=(6,3.8) )
ax = fig.add_subplot( 1, 1, 1 )
ax.spines['right'].set_visible(False)
ax.spines['top'].set_visible(False)

213
statistics/lecture/statistics-chapter.tex
View File

@@ -1,217 +1,8 @@
\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}
\input{../../header}
%%%% 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{red!60!black},
keywordstyle=\color{blue!50!black},
stringstyle=\color{green!50!black},
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}}
\lstset{inputpath=../code}
\graphicspath{{figures/}}

28
statistics/lecture/statistics.tex
View File

@@ -53,7 +53,7 @@
{Schreibe eine Funktion, die den Median eines Vektors zur\"uckgibt.}
\end{exercise}
\code{matlab} stellt die Funktion \code{median()} zur Berechnung des Medians bereit.
\matlab{} stellt die Funktion \code{median()} zur Berechnung des Medians bereit.
\begin{exercise}[checkmymedian.m]
\tr{Write a script that tests whether your median function really
@@ -70,24 +70,24 @@
\caption{\label{quartilefig} Median und Quartile einer Normalverteilung.}
\end{figure}
\begin{definition}[\tr{quartile}{Quartile}]
Die Quartile Q1, Q2 und Q3 unterteilen die Daten in vier gleich
gro{\ss}e Gruppen, die jeweils ein Viertel der Daten enthalten.
Das mittlere Quartil entspricht dem Median.
\end{definition}
% \begin{definition}[\tr{quartile}{Quartile}]
% Die Quartile Q1, Q2 und Q3 unterteilen die Daten in vier gleich
% gro{\ss}e Gruppen, die jeweils ein Viertel der Daten enthalten.
% Das mittlere Quartil entspricht dem Median.
% \end{definition}
\begin{exercise}[quartiles.m]
\tr{Write a function that computes the first, second, and third quartile of a vector.}
{Schreibe eine Funktion, die das erste, zweite und dritte Quartil als Vektor zur\"uckgibt.}
\end{exercise}
% \begin{exercise}[quartiles.m]
% \tr{Write a function that computes the first, second, and third quartile of a vector.}
% {Schreibe eine Funktion, die das erste, zweite und dritte Quartil als Vektor zur\"uckgibt.}
% \end{exercise}
\section{\tr{Histogram}{Histogramm}}
Histogramme z\"ahlen die H\"aufigkeit $n_i$ des Auftretens von
$N=\sum_{i=1}^M n_i$ Messwerten in $M$ Messbereichsklassen $i$ (Bins).
Die Klassen unterteilen den Wertebereich meist in angrenzende und
gleich gro{\ss}e Intervalle. Histogramme sch\"atzen die
Wahrscheinlichkeitsverteilung der Messwerte ab.
gleich gro{\ss}e Intervalle. Histogramme k\"onnen verwendet werden, um die
Wahrscheinlichkeitsverteilung der Messwerte abzusch\"atzen.
\begin{exercise}[rollthedie.m]
\tr{Write a function that simulates rolling a die $n$ times.}
@@ -99,7 +99,7 @@ Wahrscheinlichkeitsverteilung der Messwerte ab.
the plain hist(x) function, force 6 bins via hist( x, 6 ), and set
meaningfull bins positions.} {Plotte Histogramme von 20, 100, und
1000-mal w\"urfeln. Benutze \code{hist(x)}, erzwinge sechs Bins
mit \code{hist(x,6)}, und setze selbst sinnvolle Bins. Normiere
mit \code{hist(x,6)}, oder setze selbst sinnvolle Bins. Normiere
anschliessend das Histogram auf geeignete Weise.}
\end{exercise}
@@ -216,7 +216,7 @@ Korrelationskoeffizient
(x-\langle x \rangle)(y-\langle y \rangle) \rangle}{\sqrt{\langle
(x-\langle x \rangle)^2} \rangle \sqrt{\langle (y-\langle y
\rangle)^2} \rangle} \] quantifiziert einfache lineare
Zusammenh\"ange. Perfekt korrelierte Variablen ergeben einen
Zusammenh\"ange \matlabfun{corr}. Perfekt korrelierte Variablen ergeben einen
Korrelationskoeffizienten von $+1$, antikorrelierte Daten einen
Korrelationskoeffizienten von $-1$ und nicht korrelierte Daten einen
Korrelationskoeffizienten nahe 0 (\figrefb{correlationfig}).