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climpred.metrics._brier_score

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climpred.metrics._brier_score#

climpred.metrics._brier_score(forecast: Dataset, verif: Dataset, dim: str | List[str] | None = None, **metric_kwargs: Any) → Dataset[source]#

Brier Score for binary events.

The Mean Square Error (mse) of probabilistic two-category forecasts where the verification data are either 0 (no occurrence) or 1 (occurrence) and forecast probability may be arbitrarily distributed between occurrence and non-occurrence. The Brier Score equals zero for perfect (single-valued) forecasts and one for forecasts that are always incorrect.

BS(f, o) = (f_1 - o)^2,

where f_1 is the forecast probability of o=1.

Note

The Brier Score requires that the observation is binary, i.e., can be described as one (a “hit”) or zero (a “miss”). So either provide a function with with binary outcomes logical in metric_kwargs or create binary verifs and probability forecasts by hindcast.map(logical).mean(“member”). This Brier Score is not the original formula given in Brier [1950].

Parameters:

  • forecast – Raw forecasts with member dimension if logical provided in metric_kwargs. Probability forecasts in [0, 1] if logical is not provided.

  • verif – Verification data without member dim. Raw verification if logical provided, else binary verification.

  • dim – Dimensions to aggregate. Requires member if logical provided in metric_kwargs``to create probability forecasts. If ``logical not provided in metric_kwargs, should not include member.

  • logical (callable) – Function with bool result to be applied to verification data and forecasts and then mean("member") to get forecasts and verification data in interval [0, 1]. see xskillscore.brier_score()

Notes

minimum

0.0

maximum

1.0

perfect

0.0

orientation

negative

References

See also

Example

Define a boolean/logical: Function for binary scoring:

>>> def pos(x):
...     return x > 0  # checking binary outcomes
...

Option 1. Pass with keyword logical: (specifically designed for PerfectModelEnsemble, where binary verification can only be created after comparison)

>>> HindcastEnsemble.verify(
...     metric="brier_score",
...     comparison="m2o",
...     dim=["member", "init"],
...     alignment="same_verifs",
...     logical=pos,
... )
<xarray.Dataset>
Dimensions:  (lead: 10)
Coordinates:
  * lead     (lead) int32 1 2 3 4 5 6 7 8 9 10
    skill    <U11 'initialized'
Data variables:
    SST      (lead) float64 0.115 0.1121 0.1363 0.125 ... 0.1654 0.1675 0.1873
Attributes:
    prediction_skill_software:     climpred https://climpred.readthedocs.io/
    skill_calculated_by_function:  HindcastEnsemble.verify()
    number_of_initializations:     64
    number_of_members:             10
    alignment:                     same_verifs
    metric:                        brier_score
    comparison:                    m2o
    dim:                           ['member', 'init']
    reference:                     []
    logical:                       Callable

Option 2. Pre-process to generate a binary multi-member forecast and binary verification product:

>>> HindcastEnsemble.map(pos).verify(
...     metric="brier_score",
...     comparison="m2o",
...     dim=["member", "init"],
...     alignment="same_verifs",
... )
<xarray.Dataset>
Dimensions:  (lead: 10)
Coordinates:
  * lead     (lead) int32 1 2 3 4 5 6 7 8 9 10
    skill    <U11 'initialized'
Data variables:
    SST      (lead) float64 0.115 0.1121 0.1363 0.125 ... 0.1654 0.1675 0.1873
Attributes:
    prediction_skill_software:     climpred https://climpred.readthedocs.io/
    skill_calculated_by_function:  HindcastEnsemble.verify()
    number_of_initializations:     64
    number_of_members:             10
    alignment:                     same_verifs
    metric:                        brier_score
    comparison:                    m2o
    dim:                           ['member', 'init']
    reference:                     []

Option 3. Pre-process to generate a probability forecast and binary verification product. because member not present in hindcast anymore, use comparison="e2o" and dim="init":

>>> HindcastEnsemble.map(pos).mean("member").verify(
...     metric="brier_score",
...     comparison="e2o",
...     dim="init",
...     alignment="same_verifs",
... )
<xarray.Dataset>
Dimensions:  (lead: 10)
Coordinates:
  * lead     (lead) int32 1 2 3 4 5 6 7 8 9 10
    skill    <U11 'initialized'
Data variables:
    SST      (lead) float64 0.115 0.1121 0.1363 0.125 ... 0.1654 0.1675 0.1873
Attributes:
    prediction_skill_software:     climpred https://climpred.readthedocs.io/
    skill_calculated_by_function:  HindcastEnsemble.verify()
    number_of_initializations:     64
    alignment:                     same_verifs
    metric:                        brier_score
    comparison:                    e2o
    dim:                           init
    reference:                     []
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