In a forecasting problem, we have
- $\mathcal P$, the priors, e.g., price and demand is negatively correlated,
- $\mathcal D$, available dataset,
- $Y$, the observations, and
- $F$, the forecasts.
Under a probabilistic view, a forecaster will find out or approximate a CDF $\mathcal F$ such that1
$$ \mathcal F(Y\vert \mathcal D, \mathcal P) \to F. $$
Naively speaking, once the density $\rho(F, Y)$ is determined or estimated, a probabilistic forecaster can be formed. The joint probability of $(F, Y)$ is our prediction space.
L Ma (2022). 'Prediction Space in Forecasting', Datumorphism, 04 April. Available at: https://datumorphism.leima.is/cards/forecasting/prediction-space/.