dixon_coles_correlation_term can return nan values

[jack89roberts]

Example data and script that gives me a few nans below. Was generated with a model using one and a half seasons of data and predicting the probability of Man City 0 - Aston Villa 1:

inputs.pkl.zip

import pickle
from bpl._util import dixon_coles_correlation_term
import numpy as np
import jax.numpy as jnp

with open("inputs.pkl", "rb") as f:
    inputs = pickle.load(f)

corr_term = dixon_coles_correlation_term(
    inputs["home_goals"],
    inputs["away_goals"],
    jnp.array(inputs["expected_home_goals"]),
    jnp.array(inputs["expected_away_goals"]),
    jnp.array(inputs["corr_coef"]),
)
print(np.any(np.isnan(corr_term)))

[jack89roberts]

After investigating a bit more. The Dixon-Coles paper has the constraint:

max(- 1/lambda, - 1/mu) < rho < min(1 / (lambda * mu), 1)

This constraint is violated occasionally, in particular at the lower end. It looks to me like bpl has much narrower priors on rho than bpl-next? Maybe that's the issue?

[jack89roberts]

More likely for teams with only a small number of match results in the input data (e.g. newly promoted teams) / when using less data in general. Quickly played with priors but didn't seem to make much difference.

[jack89roberts]

#7 just sidesteps the problem by setting negative arguments to jnp.log to 0.