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fedhere edited section_Requirements_We_want_the__.tex
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\section{Requirements}
We want the interpolation
to: to
\begin{enumerate}
\item{{\b \item{{\bf Capture the diversity in the SN sample:} Using a non parametric model allows me to capture peculiar a behavior. I fit the lightcurves with Gaussian Processes using the
\tt{george} \tt{Python} {\tt george} {\tt Python} module.}
\item{{\b \item{{\bf Capture the early time variability, and the late time smoothness:}
Since variability is expected to be larger at early times, I fit the time in logarithm space.}
\item{{\b \item{{\bf Fit the observed datapoints:} this is taken care by a $\chi^2$ minimization.}
\item{{\b \item{{\bf Maintain the smoothness requirement, while the uncertainties may be underestimated or overestimated, and fill gaps with simple extrapolations: linear or nearly linear, so as to not to over-interpret the data:} The smoothness requirement can be enforced by minimizing the second derivative of the fit.}
\end{enumerate}
I choose a square exponential kernel (\tt{ExpSquaredKernel} in \ttt{george}) $$k(d)=θ_1^2 \exp(\frac{−d^2}{θ_2^2})$$. I choose the hypermarameters $θ_1^2$ and $θ_2^2$.