Here R t are appropriately sized (here -2 × 2) prior variancecovariance matrices, containing the prior variance scaling between σ 2 t and linear coefficients of the model. We chose R t to be the identity matrices, prior means for linear terms b t0 = (0.5, 0) T , and both shape and scale parameters α t and γ t were set to 1. Regularization parameters τ 2 t = 10 -5 were chosen to resolve any computational singularity issues when inverting Σ t . After the data y t is available at level t = 1, 2, the posterior joint distributions of the parameters are also normal-inverse-gamma: