Bayesian Sports Ranking with PyMC3

bayes_rank.py

import pymc3 as pm
from theano import tensor as tt
import arviz as az
import numpy as np

scores = np.array([1,1,1,0,0,0
    ]).flatten()

games = [(0,1), (0,2), (0,3),
         (1,2), (1,3),
         (3,4)]

with pm.Model() as model:
    z_team = pm.Normal("team", mu=0, sigma=1, shape=(5,))
    # Transformed parameter
    deltas = []
    for left, right in games:
      team_left = z_team[left,]
      team_right = z_team[right,] 
      deltas.append(team_left - team_right)
    
    thetas = pm.Deterministic("theta", tt.nnet.sigmoid(deltas))   
    # Likelihood
    kij = pm.Bernoulli("kij", p=thetas, observed=scores)
    trace = pm.sample(chains=4, )

az.plot_trace(trace, var_names=["team", "theta"] ,compact=False)