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.

Planted: by ;