Rational causal induction from events in time

A longstanding focus in the causal learning literature has been on inferring causal relations from contingencies, where these abstract away from time by collating independent instances or by aggregating over regularly demarcated trials. In contrast, individual causal learners encounter events in their daily lives that occur in a continuous temporal flow with no such demarcation. Consequently, the process of learning causal relationships in naturalistic environments is comparatively less understood. In this paper, we lay out a rational framework that foregrounds the role of time in causal learning. We work within the Bayesian rational analysis tradition, starting by considering how causal relations induce dependence between events in continuous time and how this can be modeled by stochastic processes from the Poisson--Gamma distribution family. We derive the qualitative signatures of causal influence, and the general computations needed to infer structure from temporal patterns. We show that this rational account can parsimoniously explain the human preference for causal models that invoke shorter, more reliable and more predictable causal influences. Furthermore, we show this provides a unifying explanation for human judgments across a wide variety of tasks in reanalysis of seven experimental datasets. We anticipate the framework will help researchers better understand the many manifestations of continuous-time causal learning across human cognition and the tasks that probe it, from explicit causal structure induction settings to implicit associative or reinforcement learning settings.