Decompositions of Proper Scores
نویسنده
چکیده
Scoring rules are an important tool for evaluating the performance of probabilistic forecasts. A popular example is the Brier score, which allows for a decomposition into terms related to the sharpness (or information content) and to the reliability of the forecast. This feature renders the Brier score a very intuitive measure of forecast quality. In this paper, it is demonstrated that all strictly proper scoring rules allow for a similar decomposition into reliability and sharpness related terms. This finding underpins the importance of proper scores and yields further credence to the practice of measuring forecast quality by proper scores. Furthermore, the effect of averaging multiple probabilistic forecasts on the score is discussed. It is well known that the Brier score of a mixture of several forecasts is never worse that the average score of the individual forecasts. This property hinges on the convexity of the Brier score, a property not universal among proper scores. Arguably, this phenomenon portends epistemological questions which require clarification.
منابع مشابه
Infinite-dimensional versions of the primary, cyclic and Jordan decompositions
The famous primary and cyclic decomposition theorems along with the tightly related rational and Jordan canonical forms are extended to linear spaces of infinite dimensions with counterexamples showing the scope of extensions.
متن کاملProper generalized decomposition for nonlinear convex problems in tensor Banach spaces
Tensor-based methods are receiving a growing interest in scienti c computing for the numerical solution of problems de ned in high dimensional tensor product spaces. A family of methods called Proper Generalized Decompositions methods have been recently introduced for the a priori construction of tensor approximations of the solution of such problems. In this paper, we give a mathematical analy...
متن کاملConvergence and comparison theorems for single and double decompositions of rectangular matrices
Different convergence and comparison theorems for proper regular splittings and proper weak regular splittings are discussed. The notion of double splitting is also extended to rectangular matrices. Finally, convergence and comparison theorems using this notion are presented.
متن کاملBerge trigraphs
A graph is Berge if no induced subgraph of it is an odd cycle of length at least five or the complement of one. In joint work with Robertson, Seymour, and Thomas we recently proved the Strong Perfect Graph Theorem, which was a conjecture about the chromatic number of Berge graphs. The proof consisted of showing that every Berge graph either belongs to one of a few basic classes, or admits one o...
متن کامل