Summary: 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. Information Set $\mathcal A$
The priors $\mathcal D$ and the available data $\mathcal P$ can be summarized together as the information set $\mathcal A$. 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.