build_ambric_model()

Build the AMBRIC Bayesian state-space model.

Usage

build_ambric_model(
    y_uk, y_annual, factors, macro, bridge_signal, region_q_on_q=None
)

The exogenous mean for latent regional growth is:

mu_exog[t,r] = Lambda[r] @ F[t] + Gamma[r] @ X[t] + delta_r * s[t,r]

where s[t,r] is the quarterly bridge signal from XGBoost + MIDAS. delta_r has a hierarchical shrinkage prior centred at zero.

Parameters

y_uk: npt.NDArray[np.float64]: UK quarterly growth rates, shape (T,).
y_annual: npt.NDArray[np.float64]: Regional annual growth rates, shape (T, R).
factors: npt.NDArray[np.float64]: Extracted factors, shape (T, K).
macro: npt.NDArray[np.float64]: Macro UK series, shape (T, M).
bridge_signal: npt.NDArray[np.float64]: Quarterly bridge signal, shape (T, R).
region_q_on_q: npt.NDArray[np.float64] | None = None: Optional published quarterly regional growth rates, shape (T, R) with NaN in unobserved cells. Values must be decimal growth rates (e.g. 0.005 for 0.5%). When supplied, y_reg is built as a hybrid pm.Deterministic: at every (t, r) with an observed value, y_reg[t, r] is hard-clamped to that value; at NaN cells, y_reg[t, r] equals the sampled latent y_reg_free[t, r]. The clamped values then propagate through the UK aggregation, annual aggregation, and AR(1) dynamics, informing unobserved neighbours rather than competing with them through a likelihood term. Defaults to None (no clamp — backwards compatible).