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[likelihood] updated exercise

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Jan Benda 2019-12-16 08:56:38 +01:00
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likelihood/exercises/exercises01.tex
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@ -15,7 +15,7 @@
\else \else
\newcommand{\stitle}{} \newcommand{\stitle}{}
\fi \fi
\header{{\bfseries\large Exercise 12\stitle}}{{\bfseries\large Maximum likelihood}}{{\bfseries\large January 7th, 2019}} \header{{\bfseries\large Exercise 11\stitle}}{{\bfseries\large Maximum likelihood}}{{\bfseries\large January 7th, 2020}}
\firstpagefooter{Prof. Dr. Jan Benda}{Phone: 29 74573}{Email: \firstpagefooter{Prof. Dr. Jan Benda}{Phone: 29 74573}{Email:
jan.benda@uni-tuebingen.de} jan.benda@uni-tuebingen.de}
\runningfooter{}{\thepage}{} \runningfooter{}{\thepage}{}
@ -115,7 +115,7 @@ of the standard deviation.
The product eventually gets smaller than the precision of the The product eventually gets smaller than the precision of the
floating point numbers support. Therefore for $n=1000$ the products floating point numbers support. Therefore for $n=1000$ the products
becomes zero. Using the logarithm avoids this numerical problem. become zero. Using the logarithm avoids this numerical problem.
\end{solution} \end{solution}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
@ -140,8 +140,8 @@ standard deviation $\sigma_i$:
line through the origin with a given slope. Use the function from line through the origin with a given slope. Use the function from
\pref{mleslopefunc} to compute the slope from the generated data. \pref{mleslopefunc} to compute the slope from the generated data.
Compare the computed slope with the true slope that has been used to Compare the computed slope with the true slope that has been used to
generate the data. Plot the data togehther with the line from which generate the data. Plot the data together with the line from which
the data were generated and the maximum-likelihood fit. the data were generated as well as the maximum-likelihood fit.
\begin{solution} \begin{solution}
\lstinputlisting{mlepropfit.m} \lstinputlisting{mlepropfit.m}
\includegraphics[width=1\textwidth]{mlepropfit} \includegraphics[width=1\textwidth]{mlepropfit}
@ -169,9 +169,9 @@ standard deviation $\sigma_i$:
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\question \qt{Maximum-likelihood-estimation of a probability-density function} \question \qt{Maximum-likelihood-estimation of a probability-density function}
Many probability-density functions have parameters that cannot be Many probability-density functions have parameters that cannot be
computed directly from the data, like, for example, the mean of computed directly from the data as it is the case for the mean of
normally-distributed data. Such parameter need to be estimated by normally-distributed data. Such parameter need to be estimated
means of the maximum-likelihood from the data. numerically by means of maximum-likelihood from the data.
Let us demonstrate this approach by means of data that are drawn from a Let us demonstrate this approach by means of data that are drawn from a
gamma distribution, gamma distribution,
@ -181,7 +181,7 @@ gamma distribution,
\part \label{gammaplot} Use this function to plot the \part \label{gammaplot} Use this function to plot the
probability-density function of the gamma distribution for various probability-density function of the gamma distribution for various
values of the (positive) ``shape'' parameter. Wet set the ``scale'' values of the (positive) ``shape'' parameter. Set the ``scale''
parameter to one. parameter to one.
\part Find out which \code{matlab} function generates random numbers \part Find out which \code{matlab} function generates random numbers