exoplanet_ecc_bias.py

import exoplanet as xo
import pymc3 as pm
import numpy as np
import matplotlib.pyplot as plt
import theano.tensor as tt

with pm.Model() as model:
    ecs = xo.UnitDisk("ecs", testval=np.array([1e-5, -1.e-5]))
    ecc = pm.Deterministic("ecc", tt.sqrt(tt.sum(ecs ** 2)))
    omega = pm.Deterministic("omega", tt.arctan2(ecs[1], ecs[0]))
    pp_v1 = pm.sample_prior_predictive(samples=10000)


with pm.Model() as model:
    secs = xo.UnitDisk("secs", testval=np.array([1e-5, -1.e-5]))
    ecc = pm.Deterministic("ecc", tt.sum(secs ** 2))
    omega = pm.Deterministic("omega", tt.arctan2(ecs[1], ecs[0]))
    pp_v2 = pm.sample_prior_predictive(samples=10000)

Sampling in ecosw and esinw is biased but sampling is sqrt(e)cosw and sqrt(e)sinw is fine.