From Deterministic to Probabilistic Forecasts of Water Demand

Although the WDSA 2024 Battle considers only deterministic forecasts, we aim to show that even if we limit the forecasts to the median values derived from the predictive density, probabilistic forecasts may lead to improved estimates. To this end, we used the MCP approach [1] to build the probability distribution of a future value conditional to two deterministic forecasts provided by the artificial neural network (ANN) and non-linear auto-regressive with external inputs (NARX) neural network models [2]. Probabilistic forecasts allow combining several deterministic forecasts and provide more comprehensive information, highly improving the reliability and robustness of deci- sions based on their information, as shown in several environmental disciplines, such as hydrology, meteorology and climatology. Although, early attempts were made by Alvisi and Franchini and Anele et al. [3–5], the probabilistic approaches have not yet gained popularity and widely spread use in WDN demand forecasting applications.