Using the collection of hypothetical PoP forecasts summarized in Table 8.8, a. Calculate the Brier score. b. Calculate the Brier score for (the sample) climatological forecast. c. Calculate the skill...

Using the collection of hypothetical PoP forecasts summarized in Table 8.8,

a. Calculate the Brier score.

b. Calculate the Brier score for (the sample) climatological forecast.

c. Calculate the skill of the forecasts with respect to the sample climatology.

d. Draw the reliability diagram.

For the hypothetical forecast data in Table 8.8,

a. Compute the likelihood-base rate factorization of the joint distribution p( yi, oj).

b. Draw the discrimination diagram.

c. Draw the ROC curve.

d. Test whether the area under the ROC curve is significantly greater than 1/2.