# GPLinearODEMaker.jl Documentation

GPLinearODEMaker (GLOM) is a package for finding the likelihood (and derivatives thereof) of multivariate Gaussian processes (GP) that are composed of a linear combination of a univariate GP and its derivatives.

where each X(t) is the latent GP and the qs are the time series of the outputs.

## Where to begin?

If you haven't used GLOM before, a good place to start is the "Getting Started" section. We list how to install the package as well as a simple example

## User's Guide

Using GLOM generally starts with choosing a kernel function (possibly with include_kernel)

and creating a GLO object.

Several kernel functions have been created already and are stored in src/kernels. Once one has a GLO, the covariances, likelihoods, and their derivatives can be easily calculated using GLOM

In addition, we have also provided some possible reasonable priors that can be used for the kernel hyperparameters

## Citing GLOM

If you use GPLinearODEMaker.jl in your work, please cite the following BibTeX entry

@ARTICLE{2020ApJ...905..155G,
author = {{Gilbertson}, Christian and {Ford}, Eric B. and {Jones}, David E. and {Stenning}, David C.},
title = "{Toward Extremely Precise Radial Velocities. II. A Tool for Using Multivariate Gaussian Processes to Model Stellar Activity}",
journal = {\apj},
keywords = {Exoplanet detection methods, Astronomy software, Stellar activity, Gaussian Processes regression, Time series analysis, 489, 1855, 1580, 1930, 1916, Astrophysics - Instrumentation and Methods for Astrophysics, Astrophysics - Earth and Planetary Astrophysics, Astrophysics - Solar and Stellar Astrophysics},
year = 2020,
month = dec,
volume = {905},
number = {2},
eid = {155},
pages = {155},
doi = {10.3847/1538-4357/abc627},
archivePrefix = {arXiv},
eprint = {2009.01085},
primaryClass = {astro-ph.IM},
}