What is the point of assigning a random variable to a named python variable?

Questions v5
1

Hi, I was playing with this post on Bayesian MMM.

coords = {"date": date, "fourier_mode": np.arange(2 * n_order)}

with pm.Model(coords=coords) as base_model:
    # --- coords ---
    base_model.add_coord(name="dat", values=date, mutable=True)
    base_model.add_coord(name="fourier_mode", values=np.arange(2 * n_order), mutable=False)

    # --- data containers ---
    z_scaled_ = pm.MutableData(name="z_scaled", value=z_scaled, dims="date")

    # --- priors ---
    ## intercept
    a = pm.Normal(name="a", mu=0, sigma=4)
    ## trend coefficient
    b_trend = pm.Normal(name="b_trend", mu=0, sigma=2)
    ## seasonality coefficient
    b_fourier = pm.Laplace(name="b_fourier", mu=0, b=2, dims="fourier_mode")
    ## regressor coefficient
    b_z = pm.HalfNormal(name="b_z", sigma=2)
    ## standard deviation of the normal likelihood
    sigma = pm.HalfNormal(name="sigma", sigma=0.5)
    # degrees of freedom of the t distribution
    nu = pm.Gamma(name="nu", alpha=25, beta=2)
    
    # --- model parametrization (coeff * data) ---
    trend = pm.Deterministic(name="trend", var=a + b_trend * t, dims="date")
    seasonality = pm.Deterministic(
        name="seasonality", var=pm.math.dot(fourier_features, b_fourier), dims="date"
    )
    z_effect = pm.Deterministic(name="z_effect", var=b_z * z_scaled_, dims="date")
    # expected value of the outcome
    mu = pm.Deterministic(name="mu", var=trend + seasonality + z_effect, dims="date")

    # --- likelihood ---
    pm.StudentT(name="likelihood", nu=nu, mu=mu, sigma=sigma, observed=y_scaled, dims="date")

    # --- prior samples ---
    base_model_prior_predictive = pm.sample_prior_predictive()

pm.model_to_graphviz(model=base_model)

What I was struggling with is that once I don’t assign pm.Deterministic(name="mu", var=trend + seasonality + z_effect, dims="date") to mu the code raises error in sampling step

with base_model:
    base_model_trace = pm.sample(
        nuts_sampler="numpyro",
        draws=6_000,
        chains=4,
        idata_kwargs={"log_likelihood": True},
    )
    base_model_posterior_predictive = pm.sample_posterior_predictive(
        trace=base_model_trace
    )

the above code throws the ValueError: Random variables detected in the logp graph: {a, b_fourier, b_z, b_trend}.

Is there anyone can help me with why this happens?

2

When you don’t assign mu you must be passing another mu variable to your likelihood variable, which probably belongs to an earlier model in the local scope.