Examples#

Executed end-to-end and re-run in CI with reduced sampling settings.

  • Univariate forecasting — weekly BART ridership with a random-walk local level, annual Fourier seasonality, and a Student-T likelihood; ADVI, CRPS evaluation, and a rolling-origin backtest.

  • Hierarchical forecasting — hourly arrivals to one BART station from all 50 origins at once: batch dims, per-series levels and weekly seasonality, shared scales.

  • Electricity demand with covariates — Victoria hourly demand with daily/weekly seasonality and a quadratic temperature response; forecasting with full-horizon covariates.

  • Exponential smoothing in state-space form — a damped Holt-Winters single-source-of-error recursion written with the shared ssoe recursion helper, fit with NUTS.

  • Local level two ways — scan-based Markov latents vs. the pymc-extras statespace backend on the same model: posterior quality, runtime, and a shared backtest.

  • Retail demand under stockouts — censored demand on the FreshRetailNet-50K panel: a hierarchical damped-trend model with a floored saturating availability factor, batched predictive sampling, and a counterfactual demand forecast at full availability.

  • ARMA forecasting — one observation/error recursion for filtering and forecasting, parameter recovery and expanding-window evaluation.

  • VAR forecasting with Impulso — a VAR(2) on quarterly US growth rates, fit by Impulso’s Minnesota prior and scored with an expanding-window backtest.

  • Intermittent demand — Bernoulli occurrence and positive Gamma quantities, stockout zeros, a naive baseline and full-availability scenarios.

  • Censored demand — an AR(2) with a right-censored normal likelihood for a known shelf cap; stockout days are gated out of the lag filter, and the same model trained as if the cap were an exact sale is the baseline.

  • Comparing inference methods — the same ARMA model fit with NUTS, ADVI, full-rank ADVI and Pathfinder; diagnostics, timing and scores.

  • M5 forecasting — top-down, bottom-up, and middle-out reconciliation of a Walmart hierarchy: official-weight check on the full panel, then the three starter-kit models fit, inspected, backtested with backtest, and scored with the competition’s weighted scaled CRPS on an 84-series panel with all 12 levels.