Updates for JOSS review 1 (#186)

* make batman an optional dependency for tests

* fixing citation formatting

* add a few more tool references

* adding phoebe reference

* adding a figure

joss/paper.bib

@@ -687,3 +687,77 @@ @software{jax
   version = {0.2.5},
   year    = {2018}
 }
+
+@article{parviainen15b,
+  author        = {{Parviainen}, H. and {Aigrain}, S.},
+  title         = {{LDTK: Limb Darkening Toolkit}},
+  journal       = {Monthly Notices of the Royal Astronomical Society},
+  keywords      = {gravitational lensing: micro, methods: numerical, techniques: interferometric, planets and satellites: general, binaries: eclipsing, Astrophysics - Earth and Planetary Astrophysics, Astrophysics - Instrumentation and Methods for Astrophysics, Astrophysics - Solar and Stellar Astrophysics},
+  year          = 2015,
+  month         = nov,
+  volume        = {453},
+  number        = {4},
+  pages         = {3821-3826},
+  doi           = {10.1093/mnras/stv1857},
+  archiveprefix = {arXiv},
+  eprint        = {1508.02634},
+  primaryclass  = {astro-ph.EP},
+  adsurl        = {https://ui.adsabs.harvard.edu/abs/2015MNRAS.453.3821P},
+  adsnote       = {Provided by the SAO/NASA Astrophysics Data System}
+}
+
+@article{irwin11,
+  author        = {{Irwin}, Jonathan M. and {Quinn}, Samuel N. and {Berta}, Zachory K. and {Latham}, David W. and {Torres}, Guillermo and {Burke}, Christopher J. and {Charbonneau}, David and {Dittmann}, Jason and {Esquerdo}, Gilbert A. and {Stefanik}, Robert P. and {Oksanen}, Arto and {Buchhave}, Lars A. and {Nutzman}, Philip and {Berlind}, Perry and {Calkins}, Michael L. and {Falco}, Emilio E.},
+  title         = {{LSPM J1112+7626: Detection of a 41 Day M-dwarf Eclipsing Binary from the MEarth Transit Survey}},
+  journal       = {The Astrophysical Journal},
+  keywords      = {binaries: eclipsing, stars: low-mass, Astrophysics - Solar and Stellar Astrophysics},
+  year          = 2011,
+  month         = dec,
+  volume        = {742},
+  number        = {2},
+  eid           = {123},
+  pages         = {123},
+  doi           = {10.1088/0004-637X/742/2/123},
+  archiveprefix = {arXiv},
+  eprint        = {1109.2055},
+  primaryclass  = {astro-ph.SR},
+  adsurl        = {https://ui.adsabs.harvard.edu/abs/2011ApJ...742..123I},
+  adsnote       = {Provided by the SAO/NASA Astrophysics Data System}
+}
+
+@article{southworth04,
+  author        = {{Southworth}, J. and {Maxted}, P.~F.~L. and {Smalley}, B.},
+  title         = {{Eclipsing binaries in open clusters - II. V453 Cyg in NGC 6871}},
+  journal       = {Monthly Notices of the Royal Astronomical Society},
+  keywords      = {binaries: eclipsing, binaries: spectroscopic, stars: early-type, stars: fundamental parameters, stars: individual: V453 Cyg, open clusters and associations: individual: NGC 6871, Astrophysics},
+  year          = 2004,
+  month         = jul,
+  volume        = {351},
+  number        = {4},
+  pages         = {1277-1289},
+  doi           = {10.1111/j.1365-2966.2004.07871.x},
+  archiveprefix = {arXiv},
+  eprint        = {astro-ph/0403572},
+  primaryclass  = {astro-ph},
+  adsurl        = {https://ui.adsabs.harvard.edu/abs/2004MNRAS.351.1277S},
+  adsnote       = {Provided by the SAO/NASA Astrophysics Data System}
+}
+
+@article{conroy20,
+  author        = {{Conroy}, Kyle E. and {Kochoska}, Angela and {Hey}, Daniel and {Pablo}, Herbert and {Hambleton}, Kelly M. and {Jones}, David and {Giammarco}, Joseph and {Abdul-Masih}, Michael and {Pr{\v{s}}a}, Andrej},
+  title         = {{Physics of Eclipsing Binaries. V. General Framework for Solving the Inverse Problem}},
+  journal       = {The Astrophysical Journal Supplement Series},
+  keywords      = {Eclipsing binary stars, 444, Astrophysics - Solar and Stellar Astrophysics, Astrophysics - Earth and Planetary Astrophysics, Astrophysics - Instrumentation and Methods for Astrophysics},
+  year          = 2020,
+  month         = oct,
+  volume        = {250},
+  number        = {2},
+  eid           = {34},
+  pages         = {34},
+  doi           = {10.3847/1538-4365/abb4e2},
+  archiveprefix = {arXiv},
+  eprint        = {2006.16951},
+  primaryclass  = {astro-ph.SR},
+  adsurl        = {https://ui.adsabs.harvard.edu/abs/2020ApJS..250...34C},
+  adsnote       = {Provided by the SAO/NASA Astrophysics Data System}
+}

joss/paper.md

@@ -147,8 +147,8 @@ related.
   that must be compiled for performance. These include an efficient solver for
   Kepler's equation [based on the algorithm proposed by @raposo17] and limb
   darkened transit light curves [@agol20]. Besides the implementation for
-  `PyMC3` and `Theano`, `exoplanet-core` includes implementations in `numpy`
-  [@numpy] and `jax` [@jax].
+  `PyMC3`, `exoplanet-core` includes implementations in `numpy` [@numpy] and
+  `jax` [@jax].
 - `celerite2`[^celerite2], is an updated implementation of the _celerite_
   algorithm[^celerite] [@foremanmackey17; @foremanmackey18] for scalable
   Gaussian Process regression for time series data. Like `exoplanet-core`,
@@ -157,8 +157,8 @@ related.
 - `pymc3-ext`[^pymc3-ext], includes a set of helper functions to make `PyMC3`
   more amenable to the typical astronomical data analysis workflow. For example,
   it provides a tuning schedule for `PyMC3`'s sampler [based on the method used
-  by the `Stan` project @carpenter17] that provides better performance on models
-  with correlated parameters.
+  by the `Stan` project and described by @carpenter17] that provides better
+  performance on models with correlated parameters.
 - `rebound-pymc3`[^rebound-pymc3] provides an interface between _REBOUND_
   [@rein12], _REBOUNDx_ [@tamayo20], and `PyMC3` to enable inference with full
   N-body orbit integration.
@@ -183,6 +183,14 @@ automatically executed using GitHub Actions, but at lower cadence (once a week
 and when a new release of the `exoplanet` library is made) since the runtime is
 much longer.
 
+![Some examples of datasets fit using `exoplanet`. The full analyses behind
+these examples are available on the "Case Studies" page as Jupyter notebooks.
+(left) A fit to the light curves of a transiting exoplanet observed by two
+different space-based photometric surveys: Kepler and TESS. (right) The phase
+folded radial velocity time series for an exoplanet observed from different
+observatories with different instruments, fit simultaneously using `exoplanet`.
+\label{fig:figure}](figures/figure.png)
+
 # Similar tools
 
 There is a rich ecosystem of tooling available for inference with models such as
@@ -194,32 +202,35 @@ context.
 Some of the most popular tools in this space include (and note that this is far
 from a comprehensive list!) `EXOFAST` [@eastman13; @eastman19], `radvel`
 [@fulton18], `juliet` [@espinoza19], `exostriker` [@trifonov19], `PYANETI`
-[@barragan19], `allesfitter` [@guenther20], and `orbitize` [@blunt20]. These
-packages all focus on providing a high-level interface for designing models and
-then executing a fit. `exoplanet`, however, is designed to be lower level and
-more conceptually similar to tools like `batman` [@kreidberg15], `PyTransit`
-[@parviainen15], `ellc` [@maxted16], `starry` [@luger19], or `Limbdark.jl`
-[@agol20], which provide the building blocks for evaluating the models required
-for inference with exoplanet datasets. In fact, several of the higher-level
-packages listed above include these lower-level libraries as dependencies, and
-our hope is that `exoplanet` could provide the backend for future high-level
-libraries.
+[@barragan19], `allesfitter` [@guenther20], and `orbitize` [@blunt20]. Similar
+tools also exist for modeling observations of eclipsing binary systems,
+including `JKTEBOP` [@southworth04], `eb` [@irwin11], and `PHOEBE` [@conroy20].
+These packages all focus on providing a high-level interface for designing
+models and then executing a fit. `exoplanet`, however, is designed to be lower
+level and more conceptually similar to tools like `batman` [@kreidberg15],
+`PyTransit` [@parviainen15], `ldtk` [@parviainen15b], `ellc` [@maxted16],
+`starry` [@luger19], or `Limbdark.jl` [@agol20], which provide the building
+blocks for evaluating the models required for inference with exoplanet datasets.
+In fact, several of the higher-level packages listed above include these
+lower-level libraries as dependencies, and our hope is that `exoplanet` could
+provide the backend for future high-level libraries.
 
 As emphasized in the title of this paper, the main selling point of `exoplanet`
 when compared to other tools in this space is that it supports differentiation
 of all components of the model and is designed to integrate seamlessly with the
-`aesara` [@aesara; formerly known as `Theano`, @theano] automatic
-differentiation framework used by `PyMC3`. This allows the use of modern
-inference algorithms such as No U-Turn Sampling [@hoffman14] or Automatic
-Differentiation Variational Inference [@kucukelbir17]. These algorithms can have
-some computational and conceptual advantages over inference methods that do not
-use gradients, especially for high-dimensional models. The computation of gradients
+`aesara` [@aesara] automatic differentiation framework used by `PyMC3`. It is
+worth noting that `aesara` was previously known as `Theano` [@theano], so these
+names are sometimes used interchangeably in the `PyMC3` or `exoplanet`
+documentation[^theano-aesara]. This allows the use of modern inference
+algorithms such as No U-Turn Sampling [@hoffman14] or Automatic Differentiation
+Variational Inference [@kucukelbir17]. These algorithms can have some
+computational and conceptual advantages over inference methods that do not use
+gradients, especially for high-dimensional models. The computation of gradients
 is also useful for model optimization; this is necessary when, say, searching
 for new exoplanets, mapping out degeneracies or multiple modes of a posterior,
-or estimating uncertainties from a Hessian. Care has been taken to provide gradients
-which are numerically stable, and more accurate and faster to evaluate than
-finite-difference gradients which can be subject to significant numerical errors
-and require 2N computations of a model with N free parameters.
+or estimating uncertainties from a Hessian. Care has been taken to provide
+gradients which are numerically stable, and more accurate and faster to evaluate
+than finite-difference gradients.
 
 # Acknowledgements
 
@@ -243,3 +254,4 @@ Besides the software cited above, `exoplanet` is also built on top of `ArviZ`
 [^celerite]: [https://celerite.readthedocs.io](https://celerite.readthedocs.io)
 [^pymc3-ext]: [https://github.com/exoplanet-dev/pymc3-ext](https://github.com/exoplanet-dev/pymc3-ext)
 [^rebound-pymc3]: [https://github.com/exoplanet-dev/rebound-pymc3](https://github.com/exoplanet-dev/rebound-pymc3)
+[^theano-aesara]: More information about this distinction is available at [https://docs.exoplanet.codes/en/stable/user/theano/](https://docs.exoplanet.codes/en/stable/user/theano/)

tests/orbits/keplerian_test.py

@@ -15,7 +15,13 @@
 )
 from exoplanet.units import with_unit
 
+try:
+    import batman
+except ImportError:
+    batman = None
 
+
+@pytest.mark.skipif(batman is None, reason="batman is not installed")
 def test_sky_coords():
     from batman import _rsky
 
@@ -313,6 +319,7 @@ def test_in_transit_circ():
     assert np.all(inds == inds_circ)
 
 
+@pytest.mark.skipif(batman is None, reason="batman is not installed")
 def test_small_star():
     from batman import _rsky