import pymc as pm
import numpy as np

def model(data):
    ages = data['age']
    lengths = data['length']
    
    with pm.Model() as model:
        # Priors for Von Bertalanffy parameters
        # L_inf: asymptotic length. Max observed is ~2.74. 
        # A HalfNormal with sigma=2.0 allows reasonable mass above 2.74.
        L_inf = pm.HalfNormal('L_inf', sigma=2.0)
        
        # k: growth coefficient. Positive.
        k = pm.HalfNormal('k', sigma=1.0)
        
        # t0: theoretical age at length 0. Can be negative.
        t0 = pm.Normal('t0', mu=0.0, sigma=1.0)
        
        # Deterministic growth curve
        mu = L_inf * (1 - pm.math.exp(-k * (ages - t0)))
        
        # Observation noise
        sigma = pm.HalfNormal('sigma', sigma=0.2)
        
        # Likelihood
        length_obs = pm.Normal('length_obs', mu=mu, sigma=sigma, observed=lengths)
        
    return model