362 lines
11 KiB
TeX
362 lines
11 KiB
TeX
\documentclass[12pt]{report}
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%%%%% title %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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\title{\tr{Introduction to Scientific Computing}{Einf\"uhrung in die wissenschaftliche Datenverarbeitung}}
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\author{Jan Benda\\Abteilung Neuroethologie\\[2ex]\includegraphics[width=0.3\textwidth]{UT_WBMW_Rot_RGB}}
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\date{WS 15/16}
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%%%% language %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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% \newcommand{\tr}[2]{#1} % en
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% \usepackage[english]{babel}
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\newcommand{\tr}[2]{#2} % de
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\usepackage[german]{babel}
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%%%%% packages %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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\usepackage{pslatex} % nice font for pdf file
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\usepackage[breaklinks=true,bookmarks=true,bookmarksopen=true,pdfpagemode=UseNone,pdfstartview=FitH,colorlinks=true,citecolor=blue]{hyperref}
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%%%% layout %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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\usepackage[left=25mm,right=25mm,top=20mm,bottom=30mm]{geometry}
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\setcounter{tocdepth}{1}
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%%%%% section style %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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\usepackage[sf,bf,it,big,clearempty]{titlesec}
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\setcounter{secnumdepth}{1}
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%%%%% units %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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\usepackage[mediumspace,mediumqspace,Gray]{SIunits} % \ohm, \micro
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%%%%% figures %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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\usepackage{graphicx}
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\usepackage{xcolor}
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\pagecolor{white}
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% figures:
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% rules for floats:
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% captions:
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% references to figures in normal text:
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\newcommand{\Subfigsref}[2]{\Figs~\subfref{#1}{#2}}
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% references to figures within bracketed text:
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\newcommand{\figrefb}[1]{\figb~\fref{#1}}
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% references to tables:
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% references to tables in normal text:
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\newcommand{\tabsref}[1]{\tabs~\tref{#1}}
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\newcommand{\Tabsref}[1]{\Tabs~\tref{#1}}
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% references to tables within bracketed text:
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\newcommand{\tabb}{Tab.}
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\newcommand{\tabsb}{Tab.}
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\newcommand{\tabrefb}[1]{\tabb~\tref{#1}}
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\newcommand{\tabsrefb}[1]{\tabsb~\tref{#1}}
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%%%%% equation references %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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%\newcommand{\eqref}[1]{(\ref{#1})}
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\newcommand{\eqn}{\tr{Eq}{Gl}.}
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\newcommand{\Eqn}{\tr{Eq}{Gl}.}
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\newcommand{\eqns}{\tr{Eqs}{Gln}.}
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\newcommand{\Eqns}{\tr{Eqs}{Gln}.}
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\newcommand{\eqnref}[1]{\eqn~\eqref{#1}}
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\newcommand{\Eqnref}[1]{\Eqn~\eqref{#1}}
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\newcommand{\eqnsref}[1]{\eqns~\eqref{#1}}
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\newcommand{\Eqnsref}[1]{\Eqns~\eqref{#1}}
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%%%%% listings %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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\usepackage{listings}
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\lstset{
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inputpath=../code,
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basicstyle=\ttfamily\footnotesize,
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numbers=left,
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showstringspaces=false,
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language=Matlab,
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commentstyle=\itshape\color{darkgray},
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keywordstyle=\color{blue},
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stringstyle=\color{green},
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backgroundcolor=\color{blue!10},
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breaklines=true,
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breakautoindent=true,
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columns=flexible,
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frame=single,
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caption={\protect\filename@parse{\lstname}\protect\filename@base},
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captionpos=t,
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xleftmargin=1em,
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xrightmargin=1em,
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aboveskip=10pt
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}
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%%%%% math stuff: %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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\usepackage{amsmath}
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\usepackage{bm}
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\usepackage{dsfont}
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\newcommand{\naZ}{\mathds{N}}
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\newcommand{\gaZ}{\mathds{Z}}
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\newcommand{\raZ}{\mathds{Q}}
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\newcommand{\reZ}{\mathds{R}}
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\newcommand{\reZp}{\mathds{R^+}}
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\newcommand{\reZpN}{\mathds{R^+_0}}
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\newcommand{\koZ}{\mathds{C}}
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%%%%% structure: %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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\usepackage{ifthen}
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\newcommand{\code}[1]{\texttt{#1}}
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\newcommand{\source}[1]{
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\begin{flushright}
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\color{gray}\scriptsize \url{#1}
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\end{flushright}
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}
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\newenvironment{definition}[1][]{\medskip\noindent\textbf{Definition}\ifthenelse{\equal{#1}{}}{}{ #1}:\newline}%
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{\medskip}
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\newcounter{maxexercise}
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\setcounter{maxexercise}{9} % show listings up to exercise maxexercise
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\newcounter{theexercise}
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\setcounter{theexercise}{1}
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\newenvironment{exercise}[1][]{\medskip\noindent\textbf{\tr{Exercise}{\"Ubung}
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\arabic{theexercise}:}\newline \newcommand{\exercisesource}{#1}}%
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{\ifthenelse{\equal{\exercisesource}{}}{}{\ifthenelse{\value{theexercise}>\value{maxexercise}}{}{\medskip\lstinputlisting{\exercisesource}}}\medskip\stepcounter{theexercise}}
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\graphicspath{{figures/}}
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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\begin{document}
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\include{statistics}
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\end{document}
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\end{document}
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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\section{Statistics}
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What is "a statistic"? % dt. Sch\"atzfunktion
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\begin{definition}[statistic]
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A statistic (singular) is a single measure of some attribute of a
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sample (e.g., its arithmetic mean value). It is calculated by
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applying a function (statistical algorithm) to the values of the
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items of the sample, which are known together as a set of data.
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\source{http://en.wikipedia.org/wiki/Statistic}
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\end{definition}
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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\section{Data types}
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\subsection{Nominal scale}
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\begin{itemize}
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\item Binary
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\begin{itemize}
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\item ``yes/no'',
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\item ``true/false'',
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\item ``success/failure'', etc.
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\end{itemize}
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\item Categorial
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\begin{itemize}
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\item cell type (``rod/cone/horizontal cell/bipolar cell/ganglion cell''),
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\item blood type (``A/B/AB/0''),
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\item parts of speech (``noun/veerb/preposition/article/...''),
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\item taxonomic groups (``Coleoptera/Lepidoptera/Diptera/Hymenoptera''), etc.
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\end{itemize}
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\item Each observation/measurement/sample is put into one category
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\item There is no reasonable order among the categories.\\
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example: [rods, cones] vs. [cones, rods]
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\item Statistics: mode, i.e. the most common item
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\end{itemize}
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\subsection{Ordinal scale}
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\begin{itemize}
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\item Like nominal scale, but with an order
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\item Examples: ranks, ratings
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\begin{itemize}
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\item ``bad/ok/good'',
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\item ``cold/warm/hot'',
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\item ``young/old'', etc.
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\end{itemize}
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\item {\bf But:} there is no reasonable measure of {\em distance}
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between the classes
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\item Statistics: mode, median
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\end{itemize}
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\subsection{Interval scale}
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\begin{itemize}
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\item Quantitative/metric values
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\item Reasonable measure of distance between values, but no absolute zero
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\item Examples:
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\begin{itemize}
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\item Temperature in $^\circ$C ($20^\circ$C is not twice as hot as $10^\circ$C)
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\item Direction measured in degrees from magnetic or true north
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\end{itemize}
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\item Statistics:
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\begin{itemize}
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\item Central tendency: mode, median, arithmetic mean
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\item Dispersion: range, standard deviation
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\end{itemize}
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\end{itemize}
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\subsection{Absolute/ratio scale}
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\begin{itemize}
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\item Like interval scale, but with absolute origin/zero
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\item Examples:
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\begin{itemize}
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\item Temperature in $^\circ$K
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\item Length, mass, duration, electric charge, ...
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\item Plane angle, etc.
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\item Count (e.g. number of spikes in response to a stimulus)
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\end{itemize}
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\item Statistics:
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\begin{itemize}
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\item Central tendency: mode, median, arithmetic, geometric, harmonic mean
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\item Dispersion: range, standard deviation
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\item Coefficient of variation (ratio standard deviation/mean)
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\item All other statistical measures
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\end{itemize}
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\end{itemize}
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\subsection{Data types}
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\begin{itemize}
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\item Data type selects
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\begin{itemize}
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\item statistics
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\item type of plots (bar graph versus x-y plot)
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\item correct tests
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\end{itemize}
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\item Scales exhibit increasing information content from nominal
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to absolute.\\
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Conversion ,,downwards'' is always possible
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\item For example: size measured in meter (ratio scale) $\rightarrow$
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categories ``small/medium/large'' (ordinal scale)
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\end{itemize}
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\subsection{Examples from neuroscience}
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\begin{itemize}
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\item {\bf absolute:}
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\begin{itemize}
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\item size of neuron/brain
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\item length of axon
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\item ion concentration
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\item membrane potential
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\item firing rate
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\end{itemize}
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\item {\bf interval:}
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\begin{itemize}
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\item edge orientation
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\end{itemize}
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\item {\bf ordinal:}
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\begin{itemize}
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\item stages of a disease
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\item ratings
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\end{itemize}
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\item {\bf nominal:}
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\begin{itemize}
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\item cell type
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\item odor
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\item states of an ion channel
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\end{itemize}
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\end{itemize}
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