From 84a21ed91ff21abf234988299141ba0d79e9fff3 Mon Sep 17 00:00:00 2001 From: Jan Benda Date: Mon, 21 Dec 2020 14:10:15 +0100 Subject: [PATCH] [regression] added note on uniqe parameters --- .../lecture/pointprocessscetchA.eps | 120 ++++-- .../lecture/pointprocessscetchA.pdf | Bin 2786 -> 2924 bytes .../lecture/pointprocessscetchB.eps | 389 ++++++++++++------ .../lecture/pointprocessscetchB.pdf | Bin 4694 -> 4877 bytes regression/lecture/regression-chapter.tex | 7 +- 5 files changed, 360 insertions(+), 156 deletions(-) diff --git a/pointprocesses/lecture/pointprocessscetchA.eps b/pointprocesses/lecture/pointprocessscetchA.eps index 59681c9..bdf6699 100644 --- a/pointprocesses/lecture/pointprocessscetchA.eps +++ b/pointprocesses/lecture/pointprocessscetchA.eps @@ -1,7 +1,7 @@ %!PS-Adobe-2.0 EPSF-2.0 %%Title: pointprocessscetchA.tex -%%Creator: gnuplot 4.6 patchlevel 4 -%%CreationDate: Mon Dec 14 23:59:13 2020 +%%Creator: gnuplot 5.2 patchlevel 8 +%%CreationDate: Thu Dec 17 09:43:52 2020 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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 Example that fitting gets harder the more parameter you have. \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 Impoartant box: summary of fit howtos. +\item Important box: summary of fit howtos. \end{itemize} \subsection{New chapter: linear fits --- generalized linear models} \begin{itemize} \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 Higher order and cross terms +\item Link function, logistic regression \end{itemize}