Evidence-Based Bayesian Disaggregation of Aggregate Indices

Disaggregates an observed aggregate price index into sectoral components with a Bayesian state-space model in which the aggregate enters as a genuine observation density rather than as a renormalization identity. A random-walk-with-drift transition in log space (with partial pooling on the drift and the innovation scale) and an estimable cross-sectional concentration produce posterior draws of the sectoral indices with credible intervals, suitable as multiple-imputation input for downstream dynamic models. The Hamiltonian Monte Carlo engine follows Stan (Carpenter et al., 2017) ; model comparison uses Pareto Smoothed Importance Sampling Leave-One-Out cross-validation (Vehtari, Gelman and Gabry, 2017) . A closed-form linear-Gaussian Kalman/RTS smoother provides an exact, MCMC-free Bayesian alternative for the same aggregate evidence.