Hand-coded fully Bayesian MCMC solution for this model:

\[ \log \lambda_H = \mu_H + \sum_k (\omega_k I(k\ on\ ice\ H) + \delta_k I(k\ on\ ice\ A))\] \[ \log \lambda_A = \mu_A + \sum_k (\omega_k I(k\ on\ ice\ A) + \delta_k I(k\ on\ ice\ H))\]

Elastic-net style Laplace-Gaussian shrinkage for parameters grouped on position (centers, wingers, defenders, goaltenders).

Pros: Great statistical properties. Interesting findings on each position's relative contributions. Can do semi-Markov structure if we need it.

Cons: Takes way too long to run in full. No one in industry hockey will get the details of what MCMC is. Needs years of data to overcome collinearity with goaltenders.