There has been considerable interest in causal modeling in the past few years. When faced with real-life datasets, however, the nature of causes and effects become far less clear, and causal models are not always satisfactory. We will examine an alternative notion of interaction information, originally developed in information theory, whereby we examine the connections between variables noncausally in terms of information synergy and redundancy. To determine the statistical strength of discovered connections, we have integrated Bayesian statistics and information theory to obtain error bars on quantities such as mutual information. Moreover, we have explored ways of summarizing complex patterns of interactions in problems ranging from ecology to political science. The talk will be conceptual.