Energy-Constrained Bayesian Updating: An Effective Model of Resource-Dependent Belief

Bayesian inference provides a normative framework for belief updating, yet standard formulations abstract away from the resource costs of implementation. Why does the same evidence produce systematically different belief revisions under varying cognitive load, time pressure, or motivational state? This paper proposes a constrained computational model of belief updating under resource limitations, grounded in Energy-Efficiency Theory (EET). We introduce a latent resource ratio η = E˙ resp/E˙ main, where E˙ resp denotes response-related allocation (processing evidence and driving change) and E˙ main denotes maintenance-related allocation (sta bilizing current representations). Within a constrained variational framework, this yields an effective posterior q(H) ∝ p(E | H) λp0(H), where the learning rate is given by the fixed mapping λ = η/(1 +η). Standard Bayesian updating is recovered as a limiting case. The framework further distinguishes parametric updating within a fixed representational structure from structural revision of the hypothesis space itself, modeled as a barrier-crossing process governed by an effective resistance Eb. We derive model-discriminative predictions and outline a measurement perspective in which the latent variables are constrained by multiple physiological and behav ioral proxies. This paper provides a constrained, testable formal account of belief dynamics under resource limitations.