Bayesian optimization framework of fixed and adaptive smoothed seismicity models: Application to seismic hazard assessment in Kalimantan, Indonesia

Kalimantan is a low-seismicity region where sparse earthquake records limit the stability of smoothed-seismicity models. This study develops a combines fixed and adaptive Gaussian smoothing, Gaussian-process Bayesian optimization, and out-of-sample evaluation to construct rate models suitable for data-limited environments. A completeness-filtered shallow catalog (Mw ≥ 4.5, depth ≤ 50 km) from 1967–2010 is used for model construction, yielding a long-term annual seismicity rate of ∼2 events/year, while the 2011–2021 catalog provides independent testing windows. Smoothing parameters are explored through grid search and optimized by minimizing the negative Poisson log-likelihood using a Matérn Gaussian-process surrogate. Predictive performance is evaluated with CSEP spatial, count, magnitude, and conditional-likelihood tests applied to sliding windows. Epistemic uncertainty in annual rates is quantified using a conjugate Gamma–Poisson formulation, with prior strength calibrated from sensitivity analysis. Results show that moderate fixed-bandwidth models (75–100 km) and the Bayesian-optimized fixed model (c ≈ 90.8 km) provide the most stable behavior across 1-, 3-, 5-, and 10-year horizons, achieving up to 100% S/CL pass-rates at intermediate windows. Adaptive models perform well at short horizons but display greater susceptibility to small event clusters. The three selected models produce broadly consistent spatial rate fields and 475-year PGA estimates of 0.01–0.09 g across the five provincial capitals. Overall, the workflow offers a reproducible basis for constructing, optimizing, and validating seismicity-rate models in low-seismicity regions, supporting early-stage hazard screening without requiring full PSHA logic-tree implementation. • Reproducible workflow integrating smoothing, Bayesian optimization, and CSEP tests. • Fixed-bandwidth kernels (≈90–100 km) show the strongest multi-horizon stability. • Gaussian-process optimization identifies well-constrained smoothing parameters. • Gamma–Poisson posteriors quantify epistemic rate uncertainty in sparse catalogs. • Selected models yield consistent rate fields and PGA estimates across Kalimantan