每种池化规则都有其适用场景：将概率组合规则与情境和风险相匹配
Every pooling rule has its world: matching probability combination rules to situations and stakes
- Tallinn University of Technology（塔林理工大学）
机构由 AI 辅助整理，请以论文原文为准。
AI总结：
本文阐明常见概率组合规则的假设，通过蒙特卡洛实验验证规则适用性、衡量不匹配规则的后果，指出二元准确性会掩盖规则差异，且多推导下成对组合会丢失信息。
AI中文摘要：
系统常需对同一是/否问题的两个数值评估进行组合，合适的公式取决于数值的含义及来源间的关联。当适用若干替代解释中的一种时，平均法是正确的；当概率报告基于条件独立证据和共同先验时，相乘概率是正确的；而对于替代成功推导的概率，则需考虑其依赖性或共享证据。本文阐明了几种常见组合规则背后的假设，并推导了对应的组合概率。两组蒙特卡洛实验探讨了不同问题：第一，受控生成机制验证了推导所得规则在其假设成立的情境中能恢复正确概率；第二，相同机制使用对数评分和具有不同成本的阈值决策，衡量了使用不匹配规则的后果。不同池化规则在阈值1/2处可产生相同的二元决策，却赋予显著不同的概率，因此仅二元准确性可能掩盖重要差异。本文还给出了冲突证据规则的概率解释，并表明对于重叠推导，保留共享不确定前提的身份可直接计算至少存在一种推导的概率；当存在三种或更多推导时，证明概率的成对组合会丢失信息。
英文摘要：
Systems often need to combine two numerical assessments of the same yes/no question. The appropriate formula depends on what the numbers represent and on how the sources are related. Averaging is correct when one of several alternative interpretations applies; multiplying odds is correct when probability reports are based on conditionally independent evidence and a common prior; and probabilities of alternative successful derivations require their dependence or shared evidence to be taken into account. We state the assumptions behind several common combination rules and derive the corresponding combined probabilities. Two groups of Monte Carlo experiments address different questions. First, controlled generating mechanisms verify that the derived rule recovers the correct probability in the situations for which its assumptions hold. Second, the same mechanisms measure the consequences of using a mismatched rule, using logarithmic score and threshold decisions with different costs. Distinct pooling rules can produce the same binary decision at threshold 1/2 while assigning substantially different probabilities, so binary accuracy alone can conceal important differences. We also give probabilistic interpretations of conflicting-evidence rules and show that, for overlapping derivations, retaining the identities of shared uncertain premises permits direct calculation of the probability that at least one derivation is available. Pairwise combination of proof probabilities loses information when there are three or more derivations.
