Marginalization and Linear Opinion Pools
研究了决策者综合多位专家主观概率分布时,若要求共识分布与边缘化操作可交换,则必须使用线性意见池(加权平均),前提是空间包含至少三个点。
Abstract Suppose a decision maker has asked a group of experts to assess subjective probability distributions over some space, and he wishes to find a consensus probability distribution as a function of these. The assumption that finding the consensus distribution commutes with marginalization of the distributions implies that the consensus must be found using a linear opinion pool (weighted average), provided the space being considered contains three or more points. Some of the consequences of this result are discussed.