Pyramid-based Bayesian modeling for high-resolution behavioral analysis

This article introduces a pyramid-based multiresolution Bayesian framework for high-resolution behavioral analysis from sparse data. By restricting covariance modeling to the coarsest layer of a parameter pyramid while using a difference pyramid for fine-scale refinement, the framework overcomes major computational and statistical challenges of traditional hierarchical Bayesian models with covariance (HBMc). The framework is evaluated against three central claims: (1) scalability through dramatically reduced computational cost, (2) precision under sparsity even with very few trials per block, and (3) improved interpretability via complementary information across resolution layers. Three Bayesian variants-Bayesian inference procedure (BIP; independent parameters), hierarchical Bayesian model with variance only (HBMv), and HBMc-were implemented in PyMC. The best-performing model, PyramidHBMc (HBMc at the top layer combined with HBMv refinement), consistently achieved the best performance (Watanabe-Akaike information criterion weight = 1.0), with the lowest root mean square error and standard deviation, reducing errors and variability by up to 74.1% and 78.5% relative to BIP across four datasets spanning one-dimensional temporal and two-dimensional spatial functions. These results directly support the three central claims and demonstrate the framework's broad applicability in perceptual and cognitive science.