# Prediction Space in Forecasting

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 that^{1}

$$ \mathcal F(Y\vert \mathcal D, \mathcal P) \to F. $$

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 L Ma;

References:

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