diff --git a/bootstrap/lecture/bootstrap-chapter.tex b/bootstrap/lecture/bootstrap-chapter.tex index a1064df..d59ac2d 100644 --- a/bootstrap/lecture/bootstrap-chapter.tex +++ b/bootstrap/lecture/bootstrap-chapter.tex @@ -18,8 +18,9 @@ \section{TODO} \begin{itemize} -\item Proper introduction of confidence intervals -\item Proper introduction of statistical tests (significance, power, etc.) +\item This chapter easily covers two lectures: +\item 1. Bootstrapping with a proper introduction of of confidence intervals +\item 2. Permutation test with a proper introduction of statistical tests (dsitrubution of nullhypothesis significance, power, etc.) \end{itemize} \end{document} diff --git a/bootstrap/lecture/bootstrap.tex b/bootstrap/lecture/bootstrap.tex index 79024fa..f23f28d 100644 --- a/bootstrap/lecture/bootstrap.tex +++ b/bootstrap/lecture/bootstrap.tex @@ -33,7 +33,7 @@ population. Rather, we draw samples (\enterm{simple random sample} then estimate a statistical measure of interest (e.g. the average length of the pickles) within this sample and hope that it is a good approximation of the unknown and immeasurable true average length of -the population (\endeterm{Populationsparameter}{population +the population (\entermde{Populationsparameter}{population parameter}). We apply statistical methods to find out how precise this approximation is. @@ -71,17 +71,18 @@ distribution of average values around the true mean of the population (\subfigref{bootstrapsamplingdistributionfig}{b}). Alternatively, we can use \enterm{bootstrapping} -(\determ{Bootstrap-Verfahren}) to generate new samples from one set of -measurements (\endeterm{Resampling}{resampling}). From these -bootstrapped samples we compute the desired statistical measure and -estimate their distribution (\endeterm{Bootstrapverteilung}{bootstrap - distribution}, \subfigref{bootstrapsamplingdistributionfig}{c}). -Interestingly, this distribution is very similar to the sampling -distribution regarding its width. The only difference is that the -bootstrapped values are distributed around the measure of the original -sample and not the one of the statistical population. We can use the -bootstrap distribution to draw conclusion regarding the precision of -our estimation (e.g. standard errors and confidence intervals). +(\determ[Bootstrap!Verfahren]{Bootstrapverfahren}) to generate new +samples from one set of measurements +(\entermde{Resampling}{resampling}). From these bootstrapped samples +we compute the desired statistical measure and estimate their +distribution (\entermde{Bootstrap!Verteilung}{bootstrap distribution}, +\subfigref{bootstrapsamplingdistributionfig}{c}). Interestingly, this +distribution is very similar to the sampling distribution regarding +its width. The only difference is that the bootstrapped values are +distributed around the measure of the original sample and not the one +of the statistical population. We can use the bootstrap distribution +to draw conclusion regarding the precision of our estimation (e.g. +standard errors and confidence intervals). Bootstrapping methods create bootstrapped samples from a SRS by resampling. The bootstrapped samples are used to estimate the sampling @@ -140,8 +141,8 @@ distribution is the standard error of the mean. \section{Permutation tests} Statistical tests ask for the probability of a measured value to originate from a null hypothesis. Is this probability smaller than the -desired \endeterm{Signifikanz}{significance level}, the -\endeterm{Nullhypothese}{null hypothesis} may be rejected. +desired \entermde{Signifikanz}{significance level}, the +\entermde{Nullhypothese}{null hypothesis} may be rejected. Traditionally, such probabilities are taken from theoretical distributions which are based on assumptions about the data. Thus the @@ -166,15 +167,15 @@ while we conserve all other statistical properties of the data. \end{figure} A good example for the application of a -\endeterm{Permutationstest}{permutaion test} is the statistical -assessment of \endeterm[correlation]{Korrelation}{correlations}. Given +\entermde{Permutationstest}{permutaion test} is the statistical +assessment of \entermde[correlation]{Korrelation}{correlations}. Given are measured pairs of data points $(x_i, y_i)$. By calculating the -\endeterm[correlation!correlation +\entermde[correlation!correlation coefficient]{Korrelation!Korrelationskoeffizient}{correlation coefficient} we can quantify how strongly $y$ depends on $x$. The correlation coefficient alone, however, does not tell whether the correlation is significantly different from a random correlation. The -\endeterm[]{Nullhypothese}{null hypothesis} for such a situation is that +\entermde{Nullhypothese}{null hypothesis} for such a situation is that $y$ does not depend on $x$. In order to perform a permutation test, we need to destroy the correlation by permuting the $(x_i, y_i)$ pairs, i.e. we rearrange the $x_i$ and $y_i$ values in a random diff --git a/header.tex b/header.tex index 0b4d53c..d626757 100644 --- a/header.tex +++ b/header.tex @@ -36,8 +36,7 @@ \usepackage[makeindex]{splitidx} \makeindex \usepackage[totoc]{idxlayout} -\newindex[\tr{Glossary}{Fachbegriffe}]{term} -\newindex[Englische Fachbegriffe]{enterm} +\newindex[Glossary]{enterm} \newindex[Deutsche Fachbegriffe]{determ} \newindex[\tr{MATLAB code}{MATLAB Code}]{mcode} \newindex[\tr{Python code}{Python Code}]{pcode} @@ -214,16 +213,25 @@ \usepackage{ifthen} % \enterm[english index entry]{} -\newcommand{\enterm}[2][]{\tr{\textit{#2}}{``#2''}\ifthenelse{\equal{#1}{}}{\tr{\protect\sindex[term]{#2}}{\protect\sindex[enterm]{#2}}}{\tr{\protect\sindex[term]{#1}}{\protect\sindex[enterm]{#1}}}} +% typeset the term in italics and add it (or the optional argument) to +% the english index. +\newcommand{\enterm}[2][]{\textit{#2}\ifthenelse{\equal{#1}{}}{\protect\sindex[enterm]{#2}}{\protect\sindex[enterm]{#1}}} % \endeterm[english index entry]{}{} -\newcommand{\endeterm}[3][]{\tr{\textit{#3}}{``#3''}\ifthenelse{\equal{#1}{}}{\tr{\protect\sindex[term]{#3}}{\protect\sindex[enterm]{#3}}}{\tr{\protect\sindex[term]{#1}}{\protect\sindex[enterm]{#1}}}\protect\sindex[determ]{#2}} +% typeset the english term in italics and add it (or the first +% optional argument) to the english index. In addition add the german +% index entry to the german index without printing it. +\newcommand{\entermde}[3][]{\textit{#3}\ifthenelse{\equal{#1}{}}{\protect\sindex[enterm]{#3}}{\protect\sindex[enterm]{#1}}\protect\sindex[determ]{#2}} % \determ[index entry]{} -\newcommand{\determ}[2][]{\tr{``#2''}{\textit{#2}}\ifthenelse{\equal{#1}{}}{\tr{\protect\sindex[determ]{#2}}{\protect\sindex[term]{#2}}}{\tr{\protect\sindex[determ]{#1}}{\protect\sindex[term]{#1}}}} +% typeset the term in quotes and add it (or the optional argument) to +% the german index. +\newcommand{\determ}[2][]{``#2''\ifthenelse{\equal{#1}{}}{\protect\sindex[determ]{#2}}{\protect\sindex[determ]{#1}}} % \codeterm[index entry]{} -\newcommand{\codeterm}[2][]{\textit{#2}\ifthenelse{\equal{#1}{}}{\protect\sindex[term]{#2}}{\protect\sindex[term]{#1}}} +% typeset the term in italics and add it (or the optional argument) to +% the english and the german index. +\newcommand{\codeterm}[2][]{\textit{#2}\ifthenelse{\equal{#1}{}}{\protect\sindex[enterm]{#2}\protect\sindex[determ]{#2}}{\protect\sindex[enterm]{#1}\protect\sindex[determ]{#1}}} \newcommand{\file}[1]{\texttt{#1}} @@ -242,10 +250,10 @@ % typeset code inline: \newcommand{\varcode}[1]{\setlength{\fboxsep}{0.5ex}\colorbox{codeback}{\texttt{#1\protect\rule[-0.1ex]{0pt}{1.6ex}}}} -% type set code and add it to the python index: +% typeset code and add it to the python index: \newcommand{\pcode}[2][]{\varcode{#2}\ifthenelse{\equal{#1}{}}{\protect\sindex[pcode]{#2}}{\protect\sindex[pcode]{#1}}} -% type set code and add it to the matlab index: +% typeset code and add it to the matlab index: \newcommand{\mcode}[2][]{\varcode{#2}\ifthenelse{\equal{#1}{}}{\protect\sindex[mcode]{#2}}{\protect\sindex[mcode]{#1}}} % XXX typeset code and put it into matlab index: diff --git a/scientificcomputing-script.tex b/scientificcomputing-script.tex index aa677cc..ef2dfd1 100644 --- a/scientificcomputing-script.tex +++ b/scientificcomputing-script.tex @@ -85,6 +85,8 @@ %\renewcommand{\texinputpath}{spectral/lecture/} %\include{spectral/lecture/spectral} +% add chapter on ROC curves + % add chapter on digital filtering % add chapter on event detection @@ -119,10 +121,9 @@ \printallsolutions %%%% indices: %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -\printindex[term] +\printindex[enterm] -\printindex[determ] % for english text -% \printindex[enterm] % for german text +\printindex[determ] %\setindexprenote{Some explanations.} %\printindex[pcode] diff --git a/statistics/lecture/statistics-chapter.tex b/statistics/lecture/statistics-chapter.tex index 8945c92..4331ed1 100644 --- a/statistics/lecture/statistics-chapter.tex +++ b/statistics/lecture/statistics-chapter.tex @@ -16,6 +16,14 @@ \include{statistics} +\section{TODO} +\begin{itemize} +\item The content of this lecture easily covers two lectures! +\item 1. mymedian and debugging, rolling a die, normalized histogram +\item 2. densities, quantiles, cumulative distribution, kernel histogram +\item Adapt the exercises to that! +\end{itemize} + \end{document} diff --git a/statistics/lecture/statistics.tex b/statistics/lecture/statistics.tex index 6a6c0b4..638136d 100644 --- a/statistics/lecture/statistics.tex +++ b/statistics/lecture/statistics.tex @@ -97,7 +97,7 @@ such that one half of the data is not greater and the other half is not smaller than the median (\figref{medianfig}). \begin{exercise}{mymedian.m}{} - Write a function \code{mymedian()} that computes the median of a vector. + Write a function \varcode{mymedian()} that computes the median of a vector. \end{exercise} \matlab{} provides the function \code{median()} for computing the median.