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fixed some index entries

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Jan Benda 2019-12-06 19:29:20 +01:00
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9
likelihood/lecture/likelihood.tex
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@ -6,8 +6,9 @@
A common problem in statistics is to estimate from a probability A common problem in statistics is to estimate from a probability
distribution one or more parameters $\theta$ that best describe the distribution one or more parameters $\theta$ that best describe the
data $x_1, x_2, \ldots x_n$. \enterm{Maximum likelihood estimators} data $x_1, x_2, \ldots x_n$. \enterm[maximum likelihood
(\enterm[mle|see{Maximum likelihood estimators}]{mle}, estimator]{Maximum likelihood estimators} (\enterm[mle|see{maximum
likelihood estimator}]{mle},
\determ{Maximum-Likelihood-Sch\"atzer}) choose the parameters such \determ{Maximum-Likelihood-Sch\"atzer}) choose the parameters such
that they maximize the likelihood of the data $x_1, x_2, \ldots x_n$ that they maximize the likelihood of the data $x_1, x_2, \ldots x_n$
to originate from the distribution. to originate from the distribution.
@ -228,7 +229,7 @@ maximized respectively.
\begin{figure}[t] \begin{figure}[t]
\includegraphics[width=1\textwidth]{mlepropline} \includegraphics[width=1\textwidth]{mlepropline}
\titlecaption{\label{mleproplinefig} Maximum likelihood estimation \titlecaption{\label{mleproplinefig} Maximum likelihood estimation
of the slope of line through the origin.}{The data (blue and of the slope of a line through the origin.}{The data (blue and
left histogram) originate from a straight line $y=mx$ trough the origin left histogram) originate from a straight line $y=mx$ trough the origin
(red). The maximum-likelihood estimation of the slope $m$ of the (red). The maximum-likelihood estimation of the slope $m$ of the
regression line (orange), \eqnref{mleslope}, is close to the true regression line (orange), \eqnref{mleslope}, is close to the true
@ -257,6 +258,7 @@ respect to $\theta$ and equate it to zero:
This is an analytical expression for the estimation of the slope This is an analytical expression for the estimation of the slope
$\theta$ of the regression line (\figref{mleproplinefig}). $\theta$ of the regression line (\figref{mleproplinefig}).
\subsection{Linear and non-linear fits}
A gradient descent, as we have done in the previous chapter, is not A gradient descent, as we have done in the previous chapter, is not
necessary for fitting the slope of a straight line, because the slope necessary for fitting the slope of a straight line, because the slope
can be directly computed via \eqnref{mleslope}. More generally, this can be directly computed via \eqnref{mleslope}. More generally, this
@ -275,6 +277,7 @@ exponential decay
Such cases require numerical solutions for the optimization of the Such cases require numerical solutions for the optimization of the
cost function, e.g. the gradient descent \matlabfun{lsqcurvefit()}. cost function, e.g. the gradient descent \matlabfun{lsqcurvefit()}.
\subsection{Relation between slope and correlation coefficient}
Let us have a closer look on \eqnref{mleslope}. If the standard Let us have a closer look on \eqnref{mleslope}. If the standard
deviation of the data $\sigma_i$ is the same for each data point, deviation of the data $\sigma_i$ is the same for each data point,
i.e. $\sigma_i = \sigma_j \; \forall \; i, j$, the standard deviation drops i.e. $\sigma_i = \sigma_j \; \forall \; i, j$, the standard deviation drops

2
plotting/lecture/plotting.tex
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@ -93,7 +93,7 @@ number of datasets.
\subsection{Simple plotting} \subsection{Simple plotting}
Creating a simple line-plot is rather easy. Assuming there exists a Creating a simple line-plot is rather easy. Assuming there exists a
variable \varcode{y} in the \codeterm{Workspace} that contains the variable \varcode{y} in the \codeterm{workspace} that contains the
measurement data it is enough to call \code[plot()]{plot(y)}. At the measurement data it is enough to call \code[plot()]{plot(y)}. At the
first call of this function a new \codeterm{figure} will be opened and first call of this function a new \codeterm{figure} will be opened and
the data will be plotted with as a line plot. If you repeatedly call the data will be plotted with as a line plot. If you repeatedly call

6
pointprocesses/lecture/pointprocesses.tex
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@ -3,7 +3,7 @@
\chapter{Spiketrain analysis} \chapter{Spiketrain analysis}
\exercisechapter{Spiketrain analysis} \exercisechapter{Spiketrain analysis}
\enterm[Action potentials]{action potentials} (\enterm{spikes}) are \enterm[action potential]{Action potentials} (\enterm{spikes}) are
the carriers of information in the nervous system. Thereby it is the the carriers of information in the nervous system. Thereby it is the
time at which the spikes are generated that is of importance for time at which the spikes are generated that is of importance for
information transmission. The waveform of the action potential is information transmission. The waveform of the action potential is
@ -110,9 +110,9 @@ describing the statistics of stochastic real-valued variables:
\frac{1}{n}\sum\limits_{i=1}^n T_i$. \frac{1}{n}\sum\limits_{i=1}^n T_i$.
\item Standard deviation of the interspike intervals: $\sigma_{ISI} = \sqrt{\langle (T - \langle T \item Standard deviation of the interspike intervals: $\sigma_{ISI} = \sqrt{\langle (T - \langle T
\rangle)^2 \rangle}$\vspace{1ex} \rangle)^2 \rangle}$\vspace{1ex}
\item \enterm{Coefficient of variation}: $CV_{ISI} = \item \enterm[coefficient of variation]{Coefficient of variation}: $CV_{ISI} =
\frac{\sigma_{ISI}}{\mu_{ISI}}$. \frac{\sigma_{ISI}}{\mu_{ISI}}$.
\item \enterm{Diffusion coefficient}: $D_{ISI} = \item \enterm[diffusion coefficient]{Diffusion coefficient}: $D_{ISI} =
\frac{\sigma_{ISI}^2}{2\mu_{ISI}^3}$. \frac{\sigma_{ISI}^2}{2\mu_{ISI}^3}$.
\end{itemize} \end{itemize}

2
programmingstyle/lecture/programmingstyle.tex
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@ -356,7 +356,7 @@ should take care when defining nested functions.
\section{Specifics when using scripts} \section{Specifics when using scripts}
A similar problem as with nested function arises when using scripts A similar problem as with nested function arises when using scripts
(instead of functions). All variables that are defined within a script (instead of functions). All variables that are defined within a script
become available in the global \codeterm{Workspace}. There is the risk become available in the global \codeterm{workspace}. There is the risk
of name conflicts, that is, a called sub-script redefines or uses the of name conflicts, that is, a called sub-script redefines or uses the
same variable name and may \emph{silently} change its content. The same variable name and may \emph{silently} change its content. The
user will not be notified about this change and the calling script may user will not be notified about this change and the calling script may

4
regression/lecture/regression.tex
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@ -76,8 +76,8 @@ large deviations.
\begin{exercise}{meanSquareError.m}{}\label{mseexercise}% \begin{exercise}{meanSquareError.m}{}\label{mseexercise}%
Implement a function \code{meanSquareError()}, that calculates the Implement a function \code{meanSquareError()}, that calculates the
\emph{mean square distance} bewteen a vector of observations ($y$) \emph{mean square distance} between a vector of observations ($y$)
and respective predictions ($y^{est}$). \pagebreak[4] and respective predictions ($y^{est}$).
\end{exercise} \end{exercise}

34
statistics/lecture/statistics.tex
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@ -147,11 +147,11 @@ data are smaller than the 3$^{\rm rd}$ quartile.
% from a normal distribution.} % from a normal distribution.}
% \end{figure} % \end{figure}
\enterm{Box-whisker plots} are commonly used to visualize and compare \enterm[box-whisker plots]{Box-whisker plots} are commonly used to
the distribution of unimodal data. A box is drawn around the median visualize and compare the distribution of unimodal data. A box is
that extends from the 1$^{\rm st}$ to the 3$^{\rm rd}$ quartile. The drawn around the median that extends from the 1$^{\rm st}$ to the
whiskers mark the minimum and maximum value of the data set 3$^{\rm rd}$ quartile. The whiskers mark the minimum and maximum value
(\figref{displayunivariatedatafig} (3)). of the data set (\figref{displayunivariatedatafig} (3)).
\begin{exercise}{univariatedata.m}{} \begin{exercise}{univariatedata.m}{}
Generate 40 normally distributed random numbers with a mean of 2 and Generate 40 normally distributed random numbers with a mean of 2 and
@ -175,7 +175,7 @@ The distribution of values in a data set is estimated by histograms
\subsection{Histograms} \subsection{Histograms}
\enterm[Histogram]{Histograms} count the frequency $n_i$ of \enterm[histogram]{Histograms} count the frequency $n_i$ of
$N=\sum_{i=1}^M n_i$ measurements in each of $M$ bins $i$ $N=\sum_{i=1}^M n_i$ measurements in each of $M$ bins $i$
(\figref{diehistogramsfig} left). The bins tile the data range (\figref{diehistogramsfig} left). The bins tile the data range
usually into intervals of the same size. The width of the bins is usually into intervals of the same size. The width of the bins is
@ -193,8 +193,9 @@ categories $i$ is the \enterm{histogram}, or the \enterm{frequency
with the expected theoretical distribution of $P=1/6$.} with the expected theoretical distribution of $P=1/6$.}
\end{figure} \end{figure}
Histograms are often used to estimate the \enterm{probability Histograms are often used to estimate the
distribution} of the data values. \enterm[probability!distribution]{probability distribution} of the
data values.
\subsection{Probabilities} \subsection{Probabilities}
In the frequentist interpretation of probability, the probability of In the frequentist interpretation of probability, the probability of
@ -254,12 +255,13 @@ In the limit to very small ranges $\Delta x$ the probability of
getting a measurement between $x_0$ and $x_0+\Delta x$ scales down to getting a measurement between $x_0$ and $x_0+\Delta x$ scales down to
zero with $\Delta x$: zero with $\Delta x$:
\[ P(x_0<x<x_0+\Delta x) \approx p(x_0) \cdot \Delta x \; . \] \[ P(x_0<x<x_0+\Delta x) \approx p(x_0) \cdot \Delta x \; . \]
In here the quantity $p(x_00)$ is a so called \enterm{probability In here the quantity $p(x_00)$ is a so called
density} that is larger than zero and that describes the \enterm[probability!density]{probability density} that is larger than
distribution of the data values. The probability density is not a zero and that describes the distribution of the data values. The
unitless probability with values between 0 and 1, but a number that probability density is not a unitless probability with values between
takes on any positive real number and has as a unit the inverse of the 0 and 1, but a number that takes on any positive real number and has
unit of the data values --- hence the name ``density''. as a unit the inverse of the unit of the data values --- hence the
name ``density''.
\begin{figure}[t] \begin{figure}[t]
\includegraphics[width=1\textwidth]{pdfprobabilities} \includegraphics[width=1\textwidth]{pdfprobabilities}
@ -280,14 +282,14 @@ the probability density over the whole real axis must be one:
\end{equation} \end{equation}
The function $p(x)$, that assigns to every $x$ a probability density, The function $p(x)$, that assigns to every $x$ a probability density,
is called \enterm{probability density function}, is called \enterm[probability!density function]{probability density function},
\enterm[pdf|see{probability density function}]{pdf}, or just \enterm[pdf|see{probability density function}]{pdf}, or just
\enterm[density|see{probability density function}]{density} \enterm[density|see{probability density function}]{density}
(\determ{Wahrscheinlichkeitsdichtefunktion}). The well known (\determ{Wahrscheinlichkeitsdichtefunktion}). The well known
\enterm{normal distribution} (\determ{Normalverteilung}) is an example of a \enterm{normal distribution} (\determ{Normalverteilung}) is an example of a
probability density function probability density function
\[ p_g(x) = \frac{1}{\sqrt{2\pi\sigma^2}}e^{-\frac{(x-\mu)^2}{2\sigma^2}} \] \[ p_g(x) = \frac{1}{\sqrt{2\pi\sigma^2}}e^{-\frac{(x-\mu)^2}{2\sigma^2}} \]
--- the \enterm{Guassian distribution} --- the \enterm{Gaussian distribution}
(\determ{Gau{\ss}sche-Glockenkurve}) with mean $\mu$ and standard (\determ{Gau{\ss}sche-Glockenkurve}) with mean $\mu$ and standard
deviation $\sigma$. deviation $\sigma$.
The factor in front of the exponential function ensures the normalization to The factor in front of the exponential function ensures the normalization to