Some ideas of topics to work on during hack session

[ericagol]

@rodluger @dfm

• Automatic differentiation could provide significant improvement in optimizing microlensing models, as well as posterior probability analysis using Hamiltonian Markov Chain Monte Carlo. A place to start might be a circular, uniform source with a single lens. This can be expressed analytically in terms of elliptic integrals, which can be handled with autodiff:

http://adsabs.harvard.edu/abs/1994ApJ...430..505W
http://adsabs.harvard.edu/abs/2002ApJ...579..430A

Another simple case would be a single, straight caustic with a limb-darkened source - this has an analytic expression in terms of elliptic integrals as well:

http://adsabs.harvard.edu/abs/1987ApJ...314..154S
http://adsabs.harvard.edu/abs/1996MNRAS.279..571A
https://arxiv.org/abs/astro-ph/9912050

• Gaussian processes could be used to detect microlensing events in the presence of quasi-periodic variability or correlated noise. Our recent implementation of a fast Gaussian process technique might help make this possible for large datasets:

https://celerite.readthedocs.io/en/stable/