Brier

Brier is a term with several distinct meanings and uses. In statistics and forecasting, Brier refers to a measure of the accuracy of probabilistic predictions, while in geography it is the name of places in North America. The word can also appear as a surname and, in botany, as an alternative spelling of "briar," a common name for thorny shrubs.

Brier score: The Brier score is calculated as the average of the squared differences between predicted probabilities and observed outcomes (0 or 1). For a set of N forecasts, p_i is the predicted probability of the event, and o_i is the actual outcome (1 if the event occurred, 0 otherwise). The score is (1/N) sum (p_i - o_i)^2. Lower scores indicate more accurate predictions. The Brier score is a proper scoring rule and is widely used to evaluate weather forecasts and other probabilistic predictions, serving as a measure of calibration.

Geographic usage: There are places named Brier in North America, such as Brier, Washington, an unincorporated community in Snohomish County, and Brier Island in Digby County, Nova Scotia.

Surname: Brier is a surname found in English-speaking countries. It may be borne by individuals in various fields, and references to people with the name appear in biographical lists and historical records.

Botany and spelling: In botanical usage, "brier" is an alternate spelling of "briar," referring to thorny shrubs or brambles. The term also appears in historical contexts and literature as a variant spelling of briar.