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exoplanet-dev / exoplanet

Fast & scalable MCMC for all your exoplanet needs!
https://docs.exoplanet.codes
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better eccentricity distribution? #61

Closed megbedell closed 5 years ago

megbedell commented 5 years ago

Currently the orbit-fitting tutorials use xo.distributions.UnitUniform or Uniform as a prior for orbital eccentricity, but this can bias the resulting maximum-likelihood estimate to high e. Are there plans to add any built-in distributions that would make better priors on eccentricity? One option might be a beta-distribution (Kipping 2014).

dfm commented 5 years ago

Not true! For example, the TESS example uses the Kipping distribution: http://exoplanet.dfm.io/en/stable/tutorials/tess/

I don't see how any choice of prior will "bias" the maximum likelihood eccentricity. It's true that the distribution of posterior means for any parameter constrained to be always positive will be "biased" high under some definition, but that's not going to be changed by choosing a different prior. If you believe that that you actually have a prior belief about the eccentricity distribution for your target, you should (by all means!) use it, but that won't save people from being careful about how they interpret the results.

megbedell commented 5 years ago

OK, that's fair. Thanks! I'd consider this issue resolved.

dfm commented 5 years ago

I do think that leaving this open and providing a few named options is worth considering.

I know of Kipping 2014 and Van Eylen et al 2019, but there must be other ones that should be included.

dfm commented 5 years ago

Or rather Kipping 2013.

dfm commented 5 years ago

Helper functions for both of these distributions are now implemented:

https://exoplanet.dfm.io/en/latest/user/api/#eccentricity-distributions