cards/time-series/crps/

[giscus[bot]]

cards/time-series/crps/

The Continuous Ranked Probability Score, known as CRPS, is a score to measure how a proposed distribution approximates the data, without knowledge about the true distributions of the data.
Definition CRPS is defined as1
$$ CRPS(P, x_a) = \int_{-\infty}^\infty \lVert P(x) - H(x - x_a) \rVert_2 dx, $$
where
$x_a$ is the true value of $x$, P(x) is our proposed cumulative distribution for $x$, $H(x)$ is the Heaviside step function $$ H(x) = \begin{cases} 1, &\qquad x=0\ 0, &\qquad x\leq 0\ \end{cases} $$
$\lVert \cdot \rVert_2$ is the L2 norm. Explain it The formula looks abstract on first sight, but it becomes crystal clear once we understand it.

https://datumorphism.leima.is/cards/time-series/crps/