Refactor interval scores and improve testing (#82)

* exclude type checking blocks from test coverage report

* fix failing tests for weighted interval score

* refactoring and fixes to interval scores

* update docs for interval scores

* improve testing for interval scores

* run formatting

docs/api/interval.md

@@ -1,34 +1,5 @@
 # Interval Score
 
-## Interval or Winkler Score
-
-For a prediction interval (PI), the interval or Winkler score is given by:
-
-$$
-\text{IS} = \begin{cases}
-    (u - l) + \frac{2}{\alpha}(l - y)  & \text{for } y < l \\
-    (u - l)                             & \text{for } l \leq y \leq u \\
-    (u - l) + \frac{2}{\alpha}(y - u)   & \text{for } y > u. \\
-\end{cases}
-$$
-
-for an $(1 - \alpha)$PI of $[l, u]$ and the true value $y$ [@gneiting_strictly_2007, @bracher2021evaluating @winkler1972decision].
-
-## Weighted Interval Score
-
-The weighted interval score (WIS) is defined as
-
-$$
-\text{WIS}_{\alpha_{0:K}}(F, y) = \frac{1}{K+0.5}(w_0 \times |y - m| + \sum_{k=1}^K (w_k \times IS_{\alpha_k}(F, y)))
-$$
-
-where $m$ denotes the median prediction, $w_0$ denotes the weight of the median prediction, $IS_{\alpha_k}(F, y)$ denotes the interval score for the $1 - \alpha$ prediction interval and $w_k$ is the according weight. The WIS is calculated for a set of (central) PIs and the predictive median [@bracher2021evaluating]. The weights are an optional parameter and default weight is the canonical weight $w_k = \frac{2}{\alpha_k}$ and $w_0 = 0.5$. For these weights, it holds that:
-
-$$
-\text{WIS}_{\alpha_{0:K}}(F, y) \approx \text{CRPS}(F, y).
-$$
-
-
 ::: scoringrules.interval_score
 
 ::: scoringrules.weighted_interval_score

pyproject.toml

@@ -58,9 +58,13 @@ dev-dependencies = [
 ]
 
 [tool.ruff]
+line-length = 88
 
 [tool.ruff.lint]
 ignore = ["E741"]
 
 [tool.coverage.run]
 omit = ["**/_gufuncs.py", "**/_gufunc.py"]
+
+[tool.coverage.report]
+exclude_also = ["if tp.TYPE_CHECKING:"]

scoringrules/_crps.py

@@ -58,7 +58,12 @@ def crps_ensemble(
     if axis != -1:
         forecasts = B.moveaxis(forecasts, axis, -1)
 
-    if not sorted_ensemble and estimator not in ["nrg", "akr", "akr_circperm", "fair"]:
+    if not sorted_ensemble and estimator not in [
+        "nrg",
+        "akr",
+        "akr_circperm",
+        "fair",
+    ]:
         forecasts = B.sort(forecasts, axis=-1)
 
     if backend == "numba":
@@ -865,7 +870,14 @@ def crps_gtclogistic(
     >>> sr.crps_gtclogistic(0.0, 0.1, 0.4, -1.0, 1.0, 0.1, 0.1)
     """
     return crps.gtclogistic(
-        observation, location, scale, lower, upper, lmass, umass, backend=backend
+        observation,
+        location,
+        scale,
+        lower,
+        upper,
+        lmass,
+        umass,
+        backend=backend,
     )
 
 
@@ -953,7 +965,14 @@ def crps_clogistic(
     lmass = stats._logis_cdf((lower - location) / scale)
     umass = 1 - stats._logis_cdf((upper - location) / scale)
     return crps.gtclogistic(
-        observation, location, scale, lower, upper, lmass, umass, backend=backend
+        observation,
+        location,
+        scale,
+        lower,
+        upper,
+        lmass,
+        umass,
+        backend=backend,
     )
 
 
@@ -990,7 +1009,14 @@ def crps_gtcnormal(
     >>> sr.crps_gtcnormal(0.0, 0.1, 0.4, -1.0, 1.0, 0.1, 0.1)
     """
     return crps.gtcnormal(
-        observation, location, scale, lower, upper, lmass, umass, backend=backend
+        observation,
+        location,
+        scale,
+        lower,
+        upper,
+        lmass,
+        umass,
+        backend=backend,
     )
 
 
@@ -1078,7 +1104,14 @@ def crps_cnormal(
     lmass = stats._norm_cdf((lower - location) / scale)
     umass = 1 - stats._norm_cdf((upper - location) / scale)
     return crps.gtcnormal(
-        observation, location, scale, lower, upper, lmass, umass, backend=backend
+        observation,
+        location,
+        scale,
+        lower,
+        upper,
+        lmass,
+        umass,
+        backend=backend,
     )
 
 
@@ -1146,7 +1179,15 @@ def crps_gtct(
     >>> sr.crps_gtct(0.0, 2.0, 0.1, 0.4, -1.0, 1.0, 0.1, 0.1)
     """
     return crps.gtct(
-        observation, df, location, scale, lower, upper, lmass, umass, backend=backend
+        observation,
+        df,
+        location,
+        scale,
+        lower,
+        upper,
+        lmass,
+        umass,
+        backend=backend,
     )
 
 
@@ -1192,7 +1233,15 @@ def crps_tt(
     >>> sr.crps_tt(0.0, 2.0, 0.1, 0.4, -1.0, 1.0)
     """
     return crps.gtct(
-        observation, df, location, scale, lower, upper, 0.0, 0.0, backend=backend
+        observation,
+        df,
+        location,
+        scale,
+        lower,
+        upper,
+        0.0,
+        0.0,
+        backend=backend,
     )
 
 
@@ -1240,7 +1289,15 @@ def crps_ct(
     lmass = stats._t_cdf((lower - location) / scale, df)
     umass = 1 - stats._t_cdf((upper - location) / scale, df)
     return crps.gtct(
-        observation, df, location, scale, lower, upper, lmass, umass, backend=backend
+        observation,
+        df,
+        location,
+        scale,
+        lower,
+        upper,
+        lmass,
+        umass,
+        backend=backend,
     )