Poisson Example

This page mirrors examples/poisson_example.py.

1 Fit A Poisson Model

import numpy as np
from pprint import pprint

from crabbymetrics import Poisson

np.set_printoptions(precision=4, suppress=True)

rng = np.random.default_rng(4)
n = 700
k = 2
beta = np.array([0.4, -0.6])
intercept = 0.2

x = rng.normal(size=(n, k))
logits = intercept + x @ beta
mu = np.exp(logits)
y = rng.poisson(mu).astype(float)

model = Poisson(alpha=0.0, max_iterations=200)
model.fit(x, y)

print("true intercept:", intercept)
print("true coef:", beta)
pprint(model.summary())

2 Prediction surfaces

For Poisson, predict_lin() returns the log-mean index and predict() exponentiates back to the conditional mean.

check = x[:8]
out = {
    "log_mu": model.predict_lin(check),
    "mu": model.predict(check),
}
pprint(out)