Bayesian Spatial Quantile Regression for Earthquake Risk Assessment and Insurance Pricing in Indonesia

Fevi Novkaniza

doi:10.31764/jtam.v9i4.32415

Bayesian Spatial Quantile Regression for Earthquake Risk Assessment and Insurance Pricing in Indonesia

Fevi Novkaniza

Abstract

Indonesia’s geographical location along the Pacific Ring of Fire makes it one of the most seismically active countries in the world, with earthquakes causing recurrent and significant economic losses. To address the need for more accurate and regionally sensitive insurance pricing, this study develops a Bayesian spatial quantile regression model that estimates the 90th percentile of earthquake-induced economic losses. Unlike conventional models that focus on mean losses, this approach captures the upper tail of the loss distribution, which is essential for designing risk financing instruments that can withstand catastrophic events. The model incorporates two main predictors: earthquake magnitude (on the Richter scale) and a provincial risk exposure index constructed from population and GDP per capita. Spatial effects are modelled using a Gaussian kernel with multiple bandwidths. Based on Leave-One-Out Cross-Validation, a bandwidth of 500 kilometers yields the best model performance, effectively capturing regional dependence in earthquake loss data. Historical data from 1930 to 2024 are used to estimate parameters via Markov Chain Monte Carlo sampling with the No-U-Turn Sampler. Results indicate that both earthquake magnitude and socioeconomic exposure are significant drivers of high-end losses. For instance, the model estimates that West Sumatra and Yogyakarta could experience annual benefit payouts exceeding USD 300,000 in high-severity scenarios. Earthquake insurance premiums are then derived using the expected payout values and a 10% premium loading factor. Premium estimates range from USD 0 to over USD 50,000 across provinces, with 20 out of 34 provinces requiring positive premiums. This study contributes a novel modelling framework that integrates quantile regression, spatial weighting, and exposure-based risk assessment. The results provide a data-driven basis for setting premiums and allocating disaster risk financing more equitably across regions. Limitations include reliance on proxy variables for exposure and the exclusion of building-level vulnerability data, which may affect precision in highly localized assessments.

Keywords

Asymetric Distribution Bayesian Spatial; Economic Losses; Gaussian Kernel; Indonesia Seismic Vulnerability; Insurance Premium.

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References

Aissaoui, O., Madani, Y., Oughdir, L., Dakkak, A., & el Allioui, Y. (2020). A Multiple Linear Regression-Based Approach to Predict Student Performance, 9–23. https://doi.org/10.1007/978-3-030-36653-7_2

Alawamy, E. A, Liu, Y., & Zhao, Y. Q. (2024). Bayesian analysis for single-server Markovian queues based on the No-U-Turn Sampler. Communications in Statistics - Simulation and Computation, 53(2), 658-670. https://doi.org/10.1080/03610918.2022.2025841

Andruszkiewicz, A., & Skorupa, J. K. (2021). The cartographic visualisation of spatial data. An example of nature protection areas in the Podlaskie Voivodship (north-eastern Poland). Polish Cartographical Review, 52(3), 108–123. https://doi.org/10.2478/pcr-2020-0009

Babaud, J., Witkin, A. P., Baudin, M., & Duda, R. O. (1986). Uniqueness of the Gaussian Kernel for Scale-Space Filtering. IEEE Transactions on Pattern Analysis and Machine Intelligence, PAMI-8(1), 26–33. https://doi.org/10.1109/TPAMI.1986.4767749

Belissa, T. K. (2024). Effects of weather index insurance adoption on household food consumption and investment in agricultural inputs in Ethiopia. Journal of Agriculture and Food Research, 16, 101043, 1-12. https://doi.org/10.1016/j.jafr.2024.101043

Burton, H. V, Deierlein, G., Lallemant, D., & Lin, T. (2016). Framework for Incorporating Probabilistic Building Performance in the Assessment of Community Seismic Resilience. Journal of Structural Engineering, 142(8), C4015007. https://doi.org/10.1061/(ASCE)ST.1943-541X.0001321

Cao, S., Deng, Y., Yang, B., Lu, G., Hu, X., Mao, Y., Hu, S., & Zhu, Z. (2023). Kernel Density Derivative Estimation of Euler Solutions. Applied Sciences, 13,1784, 1-29. https://doi.org/10.3390/app13031784

Djalante, R. (2018). Review article: A systematic literature review of research trends and authorships on natural hazards, disasters, risk reduction and climate change in Indonesia. Natural Hazards and Earth System Sciences, 18(6), 1785–1810. https://doi.org/10.5194/nhess-18-1785-2018

Fischer, M., Getis, A., & Eds. (2009). Handbook of Applied Spatial Analysis: Software Tools, Methods and Applications. https://doi.org/10.1007/978-3-642-03647-7

Fuzi, M. F. M., Jemain, A. A., & Ismail, N. (2016). Bayesian quantile regression model for claim count data. Insurance: Mathematics and Economics, 66, 124–137. https://doi.org/10.1016/j.insmatheco.2015.11.004

Ghorbani, K., Salarijazi, M., Bararkhanpour, S., & Ghaleh, L. R. (2023). Comparison of Bayesian and frequentist quantile regressions in studying the trend of discharge changes in several hydrometric stations of the Gorganroud basin in Iran. Journal of Water and Climate Change, 14(10), 3753–3769. https://doi.org/10.2166/wcc.2023.305

Goda Katsuichiro and Wenzel, F. and D. J. (2021). Insurance and Reinsurance Models for Earthquake. In I. A. and P. E. and A. I. S.-K. Beer Michael and Kougioumtzoglou (Ed.), Encyclopedia of Earthquake Engineering, 1–24. Springer Berlin Heidelberg. https://doi.org/10.1007/978-3-642-36197-5_261-1

Hu, W., & Zhang, W. (2024). Flexible Bayesian quantile regression based on the generalized asymmetric Huberised-type distribution. Statistics and Computing, 34(4), 144. https://doi.org/10.1007/s11222-024-10453-1

Jarantow, S. W., Pisors, E. D., & Chiu, M. L. (2023). Introduction to the Use of Linear and Nonlinear Regression Analysis in Quantitative Biological Assays. Current Protocols, 3(6), e801. https://doi.org/10.1002/cpz1.801

Jiang, X., Li, Y., Yang, A., & Zhou, R. (2020). Bayesian semiparametric quantile regression modeling for estimating earthquake fatality risk. Empirical Economics, 58(5), 2085–2103. https://doi.org/10.1007/s00181-018-1615-4

Kennedy, L. A., Navarro, D. J., Perfors, A., & Briggs, N. (2017). Not every credible interval is credible: Evaluating robustness in the presence of contamination in Bayesian data analysis. Behavior Research Methods, 49(6), 2219–2234. https://doi.org/10.3758/s13428-017-0854-1

Kreibich, H., Botto, A., Merz, B., & Schröter, K. (2017). Probabilistic, Multivariable Flood Loss Modeling on the Mesoscale with BT-FLEMO. Risk Analysis, 37(4), 774–787. https://doi.org/10.1111/risa.12650

Li, Y., Tang, N., & Jiang, X. (2016). Bayesian approaches for analyzing earthquake catastrophic risk. Insurance: Mathematics and Economics, 68, 110-119. https://doi.org/10.1016/j.insmatheco.2016.02.004

Magzumov, Z., & Kumral, M. (2025). Application of the hierarchical Bayesian models to analyze semi-autogenous mill throughput. Minerals Engineering, 232, 109486, 1-17. https://doi.org/10.1016/j.mineng.2025.109486

Marwala, T., Mongwe, W. T., & Mbuvha, R. (2023). Introduction to Hamiltonian Monte Carlo. Hamiltonian Monte Carlo Methods in Machine Learning, 1–29. https://doi.org/10.1016/B978-0-44-319035-3.00013-6

Nishio, M., & Arakawa, A. (2019). Performance of Hamiltonian Monte Carlo and No-U-Turn Sampler for estimating genetic parameters and breeding values. Genetics Selection Evolution, 51(1), 73. https://doi.org/10.1186/s12711-019-0515-1

Ogie, R. I., James, S., Moore, A., Dilworth, T., Amirghasemi, M., & Whittaker, J. (2022). Social media use in disaster recovery: A systematic literature review. International Journal of Disaster Risk Reduction, 70, 102783, 1-18. https://doi.org/10.1016/j.ijdrr.2022.102783

Pai, J., Li, Y., Yang, A., & Li, C. (2022). Earthquake parametric insurance with Bayesian spatial quantile regression. Insurance: Mathematics and Economics, 106, 1–12. https://doi.org/10.1016/j.insmatheco.2022.04.007

Reich, B. J., Montserrat, F., & and Dunson, D. B. (2011). Bayesian Spatial Quantile Regression. Journal of the American Statistical Association, 106(493), 6–20. https://doi.org/10.1198/jasa.2010.ap09237

Shin, S., Magnan, N., Mullally, C., & Janzen, S. (2022). Demand for Weather Index Insurance among Smallholder Farmers under Prospect Theory. Journal of Economic Behavior & Organization, 202, 82–104. https://doi.org/10.1016/j.jebo.2022.07.027

Ślusarski, M., & Jurkiewicz, M. (2020). Visualisation of Spatial Data Uncertainty. A Case Study of a Database of Topographic Objects. ISPRS International Journal of Geo-Information, 9(1), 1-15. https://doi.org/10.3390/ijgi9010016

Tu, W., Lili, Y., & and Tu, J. (2025). An introduction to Bayesian geospatial analysis using a Bayesian multilevel model case study. Annals of GIS, 31(1), 29–51. https://doi.org/10.1080/19475683.2025.2451230

Weglarczyk, S. (2018). Kernel density estimation and its application. ITM Web of Conferences, 23, 37, 1-8. https://doi.org/10.1051/itmconf/20182300037

Yu, K., & Moyeed, R. A. (2001). Bayesian quantile regression. Statistics & Probability Letters, 54(4), 437–447. https://doi.org/10.1016/S0167-7152(01)00124-9

Zanoletti, A., & Bontempi, E. (2024). The impacts of earthquakes on air pollution and strategies for mitigation: a case study of Turkey. Environmental Science and Pollution Research, 31(16), 24662–24672. https://doi.org/10.1007/s11356-024-32592-8

Závadský, J., Závadská, Z., Stepniak, C., & Stępniak, A. (2019). Spatial visualisation of stakeholders based on cartographic methodology in management systems. Economic Annals-ХХI, 179(9-10), 91–104. https://doi.org/10.21003/ea.V179-08

Zhu, W., Zhang, J., Porth, L., Tan, K.S. (2025). Index-based Insurance Design for Climate and Weather Risk Management: A Review. In: Assa, H., Liu, P., Wang, S. (eds) Quantitative Risk Management in Agricultural Business. Springer Actuarial. Springer, Cham. https://doi.org/10.1007/978-3-031-80574-5_2

DOI: https://doi.org/10.31764/jtam.v9i4.32415