Fusing probabilistic information is a fundamental task in signal and data processing with relevance to many fields of technology and science. In this work, we investigate the fusion of multiple probability density functions (pdfs) of a continuous random variable or vector. Although the case of continuous random variables and the problem of pdf fusion frequently arise in multisensor signal processing, statistical inference, and machine learning, a universally accepted method for pdf fusion does not exist. The diversity of approaches, perspectives, and solutions related to pdf fusion motivates a unified presentation of the theory and methodology of the field. We discuss three different approaches to fusing pdfs. In the axiomatic approach, the fusion rule is defined indirectly by a set of properties (axioms). In the optimization approach, it is the result of minimizing an objective function that involves an information-theoretic divergence or a distance measure. In the supra-Bayesian approach, the fusion center interprets the pdfs to be fused as random observations. Our work is partly a survey, reviewing in a structured and coherent fashion many of the concepts and methods that have been developed in the literature. In addition, we present new results for each of the three approaches. Our original contributions include new fusion rules, axioms, and axiomatic and optimization-based characterizations; a new formulation of supra-Bayesian fusion in terms of finite-dimensional parametrizations; and a study of supra-Bayesian fusion of posterior pdfs for linear Gaussian models.
翻译:在与许多技术和科学领域相关的信号和数据处理中,使用概率信息是一项基本任务。在这项工作中,我们研究的是连续随机变量或矢量的多概率密度函数(pdfs)的组合。虽然连续随机变量的情况和pdf混集问题经常出现在多传感器信号处理、统计推断和机器学习中,但并不存在一种普遍接受的混混方法。与pdf混集有关的方法、观点和解决方案的多样性促使对实地的理论和方法进行统一演示。我们讨论了使用pdf的三种不同方法。在xxiomatic方法中,聚集规则由一系列特性(轴量)间接界定。在优化方法中,这是将涉及信息-理论差异或距离测量的客观功能最小化的结果。在上拜耶斯方法中,聚合中心将基于pdf的数值解释为随机观测。我们的工作是进行一项调查,以结构一致的方式审查许多关于调和流化的模型;在新版本中,对当前版本的准确性规则的每个原始模型和方法进行了分析;在文献中,将一个原始的准确性术语和最新版本的公式纳入。