User philip dawid - MathOverflow most recent 30 from http://mathoverflow.net 2013-05-19T20:30:45Z http://mathoverflow.net/feeds/user/5689 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/22851/how-would-one-extend-the-brier-score-to-an-infinite-number-of-forecasts/22856#22856 Answer by Philip Dawid for How would one extend the Brier score to an infinite number of forecasts? Philip Dawid 2010-04-28T14:31:44Z 2010-04-28T14:31:44Z <p>A general form of the Brier score, for an essentially arbitrary outcome space $\cal X$, is as follows.</p> <p>Let $q(\cdot)$ be your quoted density for a random quantity $X$, with respect to a dominating measure $\mu$ over $\cal X$. Then your score, when outcome $X=x$ is realised, is $$S(x, q(\cdot)) = \int q(t)^2 d\mu(t) - 2q(x).$$</p> <p>The Brier score is just one of an infinity of proper scoring rules. For some alternatives, see e.g.:</p> <p>Gneiting, T. and Raftery, A. E. (2007). Strictly proper scoring rules, prediction, and estimation. Journal of the American Statistical Association, 102, 359-378.<br> Dawid, A. P. (2007). The geometry of proper scoring rules. Annals of the Institute of Statistical Mathematics 59, 77-93.<br> doi:10.1007/s10463-006-0099-8</p>