Inferential Moments of Uncertain Multivariable Systems

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.