import numpy as np
import pymc as pm

seed = sum(map(ord, "Scaling the likelihood depended variables doesn't work in PyMC"))
rng = np.random.default_rng(seed)

true_mu = 100
true_sigma = 30

n_obs = 10
coords = {
    "date": np.arange(n_obs),
}

dist = pm.Normal.dist(mu=true_mu, sigma=true_sigma, shape=n_obs)
data = pm.draw(dist, random_seed=rng)

scaling = data.max()

with pm.Model(coords=coords) as model:
    mu = pm.Normal("mu")
    sigma = pm.HalfNormal("sigma")

    target = pm.Data("target", data, dims="date")
    scaled_target = target / scaling

    pm.Normal("observed", mu=mu, sigma=sigma, observed=scaled_target)