Bayesian vs. Frequentist Mixed-Effects for Regional Site Amplification

Accurate treatment of regional site effects is essential for partially non-ergodic Ground-Motion Models (GMMs). This study compares a Bayesian hierarchical regression implemented with brms to a frequentist mixed-effects formulation using lmer for estimating period-dependent site amplification. Both models adopt the same functional form with a global linear term, a nonlinear term, and region-specific random slope deviations. The analysis uses residuals from the updated Türkiye strong-motion database (SMD- TR), spanning four regions and wide ranges of VS30, magnitude, and distance. Results indicate strong agreement in global behavior: linear and nonlinear terms show similar period trends in both frameworks, and the combined regional slopes are essentially identical at all periods. The overall residual standard deviation is also nearly the same, implying comparable fit quality. Differences primarily concern decomposition and uncertainty representation. The Bayesian model resolves sharper period-dependent regional features—most notably a peak near T ≈ 0.8 s consistent with basin/edge effects—while lmer yields smoother, more conservative deviations. For median predictions, either framework is suitable because the combined coefficients and overall standard deviation coincide. For interpretation and uncertainty propagation—especially when period-dependent regional structure matters—the Bayesian approach is preferable. In addition, brms permits weakly informative priors that encode physical expectations, which stabilizes estimates in data-sparse regimes and helps prevent overfitting. Taken together, these results clarify when each framework is most appropriate: brms for physically constrained inference and robust uncertainty quantification, lmer for speed and simplicity when median predictions are the primary goal