Search

Randomness in scientific estimation is generally assumed to arise from unmeasured or uncontrolled factors. However, when combining subjective probability estimates, heterogeneity stemming from people's cognitive or information diversity is often more important than measurement noise. This paper presents a novel framework that uses partially overlapping information sources. A specific model is proposed within that framework and applied to the task of aggregating the probabilities given by a group of forecasters who predict whether an event will occur or not. Our model describes the distribution of information across forecasters in terms of easily interpretable parameters and shows how the optimal amount of extremizing of the average probability forecast (shifting it closer to its nearest extreme) varies as a function of the forecasters' information overlap. Our model thus gives a more principled understanding of the historically ad hoc practice of extremizing average forecasts., This paper has been withdrawn because it was meant to be a revision to arXiv:1406.2148, not an independent submission. This was discovered on 27 May, 2015, when preparing a replacement version to arXiv:1406.2148. This replacement will supersede both that version and the one withdrawn here

We define and study a recurrence relation in $\mathbb{Z}^3$, called the hexahedron recurrence, which is similar to the octahedron recurrence (Hirota bilinear difference equation) and cube recurrence (Miwa equation). Like these examples, solutions to the hexahedron recurrence are partition functions for configurations on a certain graph, and have a natural interpretation in terms of cluster algebras. We give an explicit correspondence between monomials in the Laurent expansions arising in the recurrence with certain double-dimer configurations of a graph. We compute limit shapes for the corresponding double-dimer configurations. The Kashaev difference equation arising in the Ising model star-triangle relation is a special case of the hexahedron recurrence. In particular this reveals the cluster nature underlying the Ising model. The above relation allows us to prove a Laurent phenomenon for the Kashaev difference equation., Nous définissons une relation sur $\mathbb{Z}^3$ appelée “hexahedron recurrence”, qui est un cousin des relations bilinéaires “octaédrale” et “cubique”. Comme ces exemples, ses solutions peuvent être décrites comme fonctions de partition pour certaines configurations d’arêtes sur un graphe planaire, et ont une interprétation naturelle en termes de clusters. Nous trouvons une correspondance explicite entre les termes dans les développements de Laurent dans cette récurrence et certains double-recouvrements par dimères du graphe sous-jacent. On calcule les formes limites.L’équation de Kashaev paraissant dans l’opération triangle-étoile du modèle d’Ising est un cas spécial de notre récurrence. Ce fait révèle la nature “cluster” du modèle d’Ising, et nous permette de montrer la propriété de Laurent pour l’équation de Kashaev.