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.

q_0(t) = m_0(t) + a_{00}X(t) + a_{01}\\dot{X}(t) + a_{02}\\ddot{X}(t)

q_1(t) = m_1(t) + a_{10}X(t) + a_{11}\\dot{X}(t) + a_{12}\\ddot{X}(t)


q_l(t) = m_l(t) + a_{l0}X(t) + a_{l1}\\dot{X}(t) + a_{l2}\\ddot{X}(t)

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

       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},
       adsurl = {},
      adsnote = {Provided by the SAO/NASA Astrophysics Data System}


All of the package functions and types can be found here

Documentation Acknowledgments

Thanks to Documenter.jl for making Julia documentation easier and Augmentor.jl for documentation inspiration.