Bayesian Inference for Market Efficiency Under Heavy Tails

ABSTRACT A Bayesian framework quantifies market efficiency under ‐stable return distributions. Measure‐theoretic foundations establish the existence and regularity of hierarchical posteriors for . A predictive mutual information score is introduced, satisfying convexity and diffeomorphism invariance under regular variation. Geometric ergodicity is established for Metropolis‐within‐Gibbs samplers. These samplers target ‐stable posteriors, with effective sample size bounds extended to heavy‐tailed targets. When applied to major financial indices from 2008 to 2023, the framework discriminates heavy‐tailed assets from predictable light‐tailed ones. It also detects efficiency breakdowns during financial crises.