Integrating Heuristics and Mental Sampling in Belief Updating

People systematically deviate from rational Bayesian standards in belief updating, displaying biases such as base-rate neglect and conservatism. Two very different types of model aim to explain these biases: simple heuristics and stochastic sampling approximations of the Bayesian solution, like the Bayesian Sampler. However, neither approach alone accounts for the variety of responses. Here we explore a hybrid Heuristic-Anchored Bayesian Sampler (HABS) which integrates simple heuristics with a Bayesian sampler. In this framework, a simple heuristic provides an initial estimate, which may then be refined through a Bayesian sampling process to approximate the ideal Bayesian posterior. Behaviour thus depends on the size of the sample: if no samples are drawn, a heuristic response is produced, but adding samples will introduce noise while increasing average judgment accuracy. Analyses of data from a new experiment (N=200) and re-analysis of data from Stengård et al., 2022 revealed that, in most conditions, this integrative approach outperformed purely heuristic or purely Bayesian models in explaining how people update their beliefs in the medical diagnosis task. Our findings suggest that people flexibly combine mental shortcuts and approximate Bayesian processes, illuminating why some responses appear purely heuristic while others reflect approximate Bayesian updating.