import pymc as pm
import numpy as np

def model(data):
    age = data['age']
    length = data['length']
    
    with pm.Model() as dugong_model:
        # Priors for the von Bertalanffy growth parameters
        # L_infinity: asymptotic length
        L_inf = pm.HalfNormal('L_inf', sigma=2)
        
        # k: growth rate
        k = pm.HalfNormal('k', sigma=1)
        
        # Observation noise
        sigma = pm.HalfNormal('sigma', sigma=0.2)
        
        # Expected length
        # Using the von Bertalanffy growth function: L(t) = L_inf * (1 - exp(-k * t))
        mu = L_inf * (1 - pm.math.exp(-k * age))
        
        # Likelihood
        likelihood = pm.Normal('likelihood', mu=mu, sigma=sigma, observed=length)
        
    return dugong_model