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[regression] added note on uniqe parameters

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This commit is contained in:
Jan Benda 2020-12-21 14:10:15 +01:00
parent 9b020bc6db
commit 84a21ed91f
5 changed files with 360 additions and 156 deletions
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120
pointprocesses/lecture/pointprocessscetchA.eps
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7
regression/lecture/regression-chapter.tex
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@ -28,18 +28,21 @@
\item Move 8.7 to this new chapter. \item Move 8.7 to this new chapter.
\item Example that illustrates the Nebenminima Problem (with error \item Example that illustrates the Nebenminima Problem (with error
surface). Maybe data generate from $1/x$ and fitted with surface). Maybe data generate from $1/x$ and fitted with
$\exp(\lambda x)$ induces local minima. $c\exp(\lambda x)$ induces local minima.
\item You need initial values for the parameter! \item You need initial values for the parameter!
\item Example that fitting gets harder the more parameter you have. \item Example that fitting gets harder the more parameter you have.
\item Try to fix as many parameters before doing the fit. \item Try to fix as many parameters before doing the fit.
\item Ensure that all parameters in the function are unique, e.g. $a e^{x-c} = be^x$.
\item How to test the quality of a fit? Residuals. $\chi^2$ test. Run-test. \item How to test the quality of a fit? Residuals. $\chi^2$ test. Run-test.
\item Impoartant box: summary of fit howtos. \item Important box: summary of fit howtos.
\end{itemize} \end{itemize}
\subsection{New chapter: linear fits --- generalized linear models} \subsection{New chapter: linear fits --- generalized linear models}
\begin{itemize} \begin{itemize}
\item Polyfit is easy: unique solution! $c x^3$ is also a linear fit. \item Polyfit is easy: unique solution! $c x^3$ is also a linear fit.
\item Example for \emph{overfitting} with polyfit of a high order (=number of data points) \item Example for \emph{overfitting} with polyfit of a high order (=number of data points)
\item Higher order and cross terms
\item Link function, logistic regression
\end{itemize} \end{itemize}