Computation-Limited Bayesian Updating: A Resource-Rational Analysis of Approximate Bayesian Inference

Data and computational capacity are essential resources for any intelligent system that update its beliefs by integrating new information. However, both data and computational resources are inherently limited. Here, we introduce a new resource-rational analysis of belief updating that formalizes these constraints using information-theoretic principles. Our analysis reveals an interaction between data and computational limitations: when computational resources are scarce, agents may struggle to fully incorporate new data. The resource-rational belief updating rule we derive provides a novel explanation for conservative Bayesian updating, where individuals tend to underweight the likelihood of new evidence. Our theory also generates predictions consistent with several process models, particularly those based on approximate Bayesian inference.