From: http://www.ecmwf.int/products/forecasts/guide/Hit_rate_and_False_alarm_rate.html

For any threshold (like

frost/no frost, rain/dry or gale/no gale) the forecast is

simplified to a yes/no statement (categorical forecast). The

observation itself is put in one of two categories (event

observed/not observed). Let H denote "hits", i.e. all correct

yes-forecasts - the event is predicted to occur and it does occur,

F false alarms, i.e. all incorrect yes-forecasts, M missed

forecasts (all incorrect no-forecasts that the event would not

occur) and Z all correct no-forecasts. Assume altogether N

forecasts of this type with H+F+M+W=N. A perfect forecast sample is

when F and M are zero. A large number of verification scores13 are computed from

these four values.

A forecast/verification table

The frequency bias

BIAS=(H+F)/(H+M), ratio of the yes forecast frequency to the yes

observation frequency.

The proportion of

correct PC=(H+Z)/N, gives the fraction of all the forecasts that

were correct. Usually it is very misleading because it credits

correct "yes" and "no" forecasts equally and it is strongly

influenced by the more common category (typically the "no"

event).

The probability of

detection POD=H/(H+M), also known as Hit Rate (HR), measures the

fraction of observed events that were correctly forecast.

The false alarm ratio

FAR=F/(H+F), gives the fraction of forecast events that were

observed to be non events.

The probability of

false detection POFD=F/(Z+F), also known as the false alarm rate,

is the measure of false alarm given the vent did not occur. POFD is

generally associated with the evaluation of probabilistic forecast

by combining it with POD into the Relative Operating Characteristic

diagram (ROC)

A very simple measure of

success of categorical forecasts is the difference POD-FAR which is

known as the Hansen-Kuiper or True Skill Score. Among other

properties, it can be easily generalised for the verification of

probabilistic forecast (see 7.4 below).

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