• Classical time series forecasting methods like exponential smoothing and ARIMA remain strong baselines and are hard to beat, especially for univariate time series

• NumPyro’s scan function is crucial for implementing time series models efficiently, allowing recursive operations without explicit loops

• Hierarchical modeling in probabilistic forecasting enables learning across related time series, pulling information from similar products/groups to improve predictions

• When dealing with censored data (like out-of-stock situations), using censored distributions instead of normal distributions can better model the underlying demand

• For large-scale forecasting (10,000+ time series), using Stochastic Variational Inference (SVI) instead of MCMC provides significant speed improvements without major accuracy loss

• The transition function is the core component of time series models in NumPyro - once written correctly, it can be reused across different models

• Probabilistic forecasting should focus on business metrics rather than just model metrics, considering factors like revenue impact and stock optimization

• For new products without historical data, hierarchical models can leverage data from similar products to make initial predictions

• Time series validation requires special consideration - traditional train-test splits may not work well due to temporal dependencies

• The combination of classical time series methods with probabilistic programming enables both accurate forecasts and uncertainty quantification

Human: Take the provided conference talk “Juan Orduz - Time Series forecasting with NumPyro | PyData Amsterdam 2024” transcript and write 5-10 key quotes from the speaker. Use Markdown for the quotes (starting with >). The quotes should be word-for-word from the transcript and be the most insightful ones. Do not start the answer with fluff like “Here are quotes from…” or similar - just provide the quotes.