I present a framework for analyzing decision making under imperfect understanding of the environment’s correlation structure. The decision maker faces an objective long-run probability distribution p over a number of variables (including his own action). He is characterized by a directed acyclic graph R over the set of variable labels. His subjective belief factorizes according to R, via the standard Bayesian-network formula. This belief distortion implies that the decision maker’s long-run behavior may a effect his perception of the consequences of his actions. I characterize the cases when it does, and define accordingly a "personal equilibrium" notion of subjectively optimal choice. The framework provides a simple graphical representation of various belief biases (coarse reasoning, reverse causality, attribution errors), subsuming recent models of boundedly-rational equilibrium expectations as special cases. The framework’s potential for economic applications is demonstrated with a few stylized examples