Prior-Likelihood Metamers to Distinguish Strategies Underlying Human Bayesian Behaviour in Perception

Abstract

Bayesian decision theory proposes that people make statistically rational decisions by combining prior knowledge with sensory information (likelihoods). This framework successfully explains many aspects of human behaviour. However, debate persists over whether people perform precise Bayesian computations (i.e., explicit Bayesian strategy) or rely on less demanding strategies - such as approximations or heuristics - that produce Bayesian-like behaviour (i.e., implicit Bayesian strategy). To address this, we examined people's sensitivity to metamers: different prior-likelihood combinations yielding identical optimal policies. An explicit Bayesian observer would show a temporary performance drop immediately after a switch of prior-likelihood combination, followed by recovery, reflecting prior updating. In two studies, we trained participants to estimate hidden target locations drawn from a Gaussian prior. On each trial, scattered dots provided likelihood information. Over time, participants learned the prior and combined it with likelihood information to infer target locations. We then covertly introduced an untrained prior-likelihood metamer. Unlike explicit Bayesian observers, participants' performance declined after the switch and persisted throughout the untrained pair presentation. This finding challenges strict Bayesian interpretations of task performance and suggests that participants rely instead on likelihood-sensitive strategy that is neither explicit Bayesian nor does it not fully integrate prior information. Our study demonstrates how metamer manipulations can distinguish behaviour that merely appears Bayesian, from behaviour genuinely produced by Bayesian computations, and calls for the use of metamers for ruling out alternative explanations of Bayesian-like behaviours.