EnsRoca: Area Under the ROC Curve

Description

Computes the area under the ROC curve given the observations. EnsRoca computes the Area Under the Curve (AUC). For ease of interpretation, EnsRocss converts the AUC to the range from -1 to 1 with zero indicating a forecast with no discrimination.

Usage

EnsRoca(ens, obs, use.easy = FALSE)
EnsRocss(ens, obs, use.easy = FALSE)

Arguments

ens: n x j matrix of n probability forecasts for j categories
obs: n x j matrix of occurence of n verifying observations in j categories
use.easy: logical, should implementation of standard errors as implemented in easyVerifcation be used (see below)?

Standard Error

If used with SpecsVerification >= 0.5, the standard errors as implemented in the function SpecsVerification::Auc are used.

If use.easy = TRUE or when used with an older version of SpecsVerification, the standard error $\sigma$ of the ROC area skill score is given by the following formula after Broecker (2012).

$$\sigma^2 = \frac{1}{3} \left(\frac{1}{N_0} + \frac{1}{N_1} + \frac{1}{N_0 N_1} \right)$$

Where $\sigma$ is the standard error, $N_1$ the number of events, and $N_0$ the number of non-events in category i.

References

Br\"ocker, J. (2012). Probability forecasts. Forecast Verification: A Practitioner's Guide in Atmospheric Science, Second Edition, 119-139.

Examples

Run this code

tm <- toymodel()

## compute ROC area for tercile forecasts using veriApply
veriApply("EnsRoca", fcst = tm$fcst, obs = tm$obs, prob = 1:2 / 3)