Rational causal induction from events in time

A longstanding focus in the causal learning literature has been on inferring causal relations from contingency data, which abstracts away from time by collating independent instances or aggregating over regularly demarcated trials. In contrast, individual causal learners encounter events in their daily lives that occur in a continuous temporal flow without distinct experimental trials. Consequently, the process of learning causal relationships in naturalistic environments remains comparatively less understood. In this paper, we develop a rational framework that foregrounds the role of time in causal learning. We work within the Bayesian rational analysis tradition, linking causal influence with dependence between events in continuous time via stochastic processes from the Poisson--Gamma distribution family. We demonstrate the qualitative differences in temporal patterns when two variables are related vs. unrelated, and the quantitative steps needed to infer causal structure from temporal patterns. We show that our rational account parsimoniously explains the human preference for causal explanations that involve shorter, more reliable and more predictable causal influences. Furthermore, we show this provides a unifying explanation for human judgments across seven experimental datasets from the causal learning literature.