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I said I would write an abstract #86

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49 changes: 37 additions & 12 deletions paper/ms.tex
Original file line number Diff line number Diff line change
Expand Up @@ -45,6 +45,7 @@
\newcommand{\eqalt}[1]{Equation~\eqref{#1}}
\newcommand{\eqlabel}[1]{\label{eq:#1}}

\newcommand{\documentname}{\textsl{Article}}
\newcommand{\sectionname}{Section}
\newcommand{\sectref}[1]{\ref{sect:#1}}
\newcommand{\Sect}[1]{\sectionname~\sectref{#1}}
Expand All @@ -66,6 +67,9 @@

\newcommand{\response}[1]{{\color{blue}#1}}

\shorttitle{gaussian processes in astronomy}
\shortauthors{foreman-mackey}

\begin{document}
\sloppy\sloppypar\raggedbottom\frenchspacing

Expand All @@ -80,21 +84,42 @@
\affiliation{Center for Computational Astrophysics, Flatiron Institute, New York, NY}

\begin{abstract}\noindent

This is an abstract.

Gaussian processes provide a flexible framework
for modeling nuisances or systematics that are unknown, non-linear functions of known
control parameters.
Examples include stochastic variability (as a function of time) of stars, wavelength-trace
or continuum calibration (as a function of wavelength) in spectrographs,
or dust (as a function of spatial position) in the Milky Way.
In this purely pedagogical \documentname, I explain what Gaussian processes are,
show examples of their use, provide specific advice for implementation, and discuss their
limitations and scope of applicability.
A Gaussian process can be thought of as a prior over a space of functions,
or a function with a formally infinite number of free parameters (a non-parametric model),
or a model for correlated Gaussian noise;
I introduce the processes through the latter point of view, but show how the multiple
views are related by showing that they can be used to deliver posterior beliefs
over continuous functions that explain noisy data.
I connect the idea of the Gaussian process to ideas (common in
data analysis) of simultaneously fitting and marginalizing out additive nuisances.
Most uses of Gaussian process in astronomy have been in the context of functions of one
or a few variables (time, or space, or wavelength); I emphasize that there might be
valuable applications in which the ambient dimension is far larger (for example, to model
nonlinear functions of thousands of elements of housekeeping data), and show some examples.
In certain limits, Gaussian processes can be physically motivated as the response
of a linear system to Gaussian white-noise forcing, which makes them interesting for
modeling finite-Q oscillations in, for example, asteroseismology; I give some examples.
Finally, I discuss ways to make Gaussian processes fast, by exploiting problem structure,
and point to relevant literature and software.
\end{abstract}

\keywords{%
%methods: data analysis
%---
%methods: statistical
%---
%asteroseismology
%---
%stars: rotation
%---
%planetary systems
asteroseismology
---
methods: data analysis
---
methods: statistical
---
methods: numerical
}

\section{Introduction}
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