Revising Previsions: A Geometric Interpretation
本文用几何方法解释个体如何根据新信息修正预估值，构建内积空间并用算子表示信息更新，适合对主观概率和统计推断几何化感兴趣的读者。
SUMMARY This paper considers the way in which an individual's previsions are changed by new information. Firstly, reasons are discussed for preferring prevision to probability as the fundamental element in the subjective formulation of statistical procedures. Then, following de Finetti, an inner product space is constructed, such that the vectors are random quantities of interest and the inner product corresponds to the previsions of the individual. The expected effect of new data is expressed by a bounded self-adjoint operator on this space. The information expected from the data is represented in terms of the eigenstructure of the operator. If the operator is compact, this representation has particularly simple form. New data impose orthogonal co-ordinate axes on the original inner-product space. The information expected about any random quantity is represented by a specified shrinkage along each axis. to any order of accuracy, all the information may be represented by a finite dimensional subspace. Finally, the geometric representation is related to more conventional, totally specified models.