This article offers a new paradigm for analyzing the behavior of uncertain multivariable systems using a set of quantities we call \emph{inferential moments}. Marginalization is an uncertainty quantification process that averages conditional probabilities to quantify the \emph{expected value} of a probability of interest. Inferential moments are higher order conditional probability moments that describe how a distribution is expected to respond to new information. Of particular interest in this article is the \emph{inferential deviation}, which is the expected fluctuation of the probability of one variable in response to an inferential update of another. We find a power series expansion of the Mutual Information in terms of inferential moments, which implies that inferential moment logic may be useful for tasks typically performed with information theoretic tools. We explore this in two applications that analyze the inferential deviations of a Bayesian Network to improve situational awareness and decision-making. We implement a simple greedy algorithm for optimal sensor tasking using inferential deviations that generally outperforms a similar greedy Mutual Information algorithm in terms of predictive probabilistic error.

翻译：本文提出了一种分析不确定多变量系统行为的新范式，该范式基于一组我们称之为“推论矩”的量。边缘化是一种不确定性量化过程，通过对条件概率进行平均来量化所关注的概率的“期望值”。推论矩是更高阶的条件概率矩，用于描述分布如何对新信息做出预期的响应。本文特别关注的是“推论偏差”，即一个变量的概率因另一个变量的推论更新而产生的期望波动。我们发现了互信息关于推论矩的幂级数展开式，这表明推论矩逻辑可能适用于通常由信息论工具完成的任务。我们通过在两个应用中探索这一发现，分析贝叶斯网络的推论偏差以提高态势感知和决策能力。我们实现了一个简单的贪心算法，利用推论偏差进行最优传感器任务分配，该算法在预测概率误差方面通常优于类似的贪心互信息算法。