Bayesian Tobit Model for Handling Left-Censored in Water Quality Assessment: A Case Study of Sunda Strait, Indonesia
DOI:
10.29303/jppipa.v12i4.13432Published:
2026-04-25Downloads
Abstract
As an archipelagic nation, Indonesia relies heavily on coastal activities that may affect marine water quality, yet studies addressing this issue remain limited, particularly in the presence of left-censored data. This study aims to evaluate an appropriate method for handling left-censored data in water quality assessment using the CCME-WQI, with a case study in the Sunda Strait. A Bayesian Tobit model was applied to account for left-censored observations and integrated with the CCME-WQI framework. For comparison, conventional substitution methods and exclude left-censored were also used. The performance of approaches was assessed based on their ability to produce reliable water quality index estimates. The results indicate that the Bayesian Tobit model provides more robust estimates than substitution methods, as it incorporates uncertainty through credible intervals and reduces potential bias. The estimated water quality index ranged from 83.8 to 92.1, classifying the water quality as “good.” In conclusion, the Bayesian Tobit model is a more reliable approach for handling left-censored environmental data and improving water quality assessment. This method is particularly relevant for routine monitoring and can be extended to other fields with similar data characteristics.
Keywords:
Bayesian-Tobit Model CCME-WQI Left-Censored Sunda Strait Water Quality AssessmentReferences
Al-Qadami, E. H. H., Razi, M. A. M., Shah, S. M. H., Mokhtar, A., Mahamud, M., Jamal, M. H., & Ismail, Z. A. (2025). Marine Water and Sediment Quality Assessment of Mainland Kedah and Langkawi Island Shorelines: A Case Study. IOP Conference Series: Earth and Environmental Science, 1453(012058), 1–11. https://doi.org/10.1088/1755-1315/1453/1/012058
Albert, D. L., Hardy, W. N., & Kemper, A. R. (2024). Effect of data censoring on thoracic injury risk curves. Traffic Injury Prevention, 25(sup1), S33–S42. https://doi.org/10.1080/15389588.2024.2405643
Bürkner, P. (2018). Advanced Bayesian Multilevel Modeling with the R Package brms. The R Journal, 10(July), 395–411. https://journal.r-project.org/articles/RJ-2018-017/RJ-2018-017.pdf
Bürkner, P. C. (2017). brms: An R package for Bayesian multilevel models using Stan. Journal of Statistical Software, 80(1), 1–28. https://doi.org/10.18637/jss.v080.i01
Canadian Council of Ministers of the Environment. (2017). CCME Water Quality Index user’s manual 2017 Update. Canadian Water Quality Guidelines for the Protection of Aquatic Life, 1–5. https://ccme.ca/en/res/wqimanualen.pdf
Chasanah, N., Armono, H. D., & Radianta, W. (2020). Pemodelan Penjalaran Tsunami Akibat Erupsi Gunung Anak Krakatau Beserta Skenario Dike, Studi Kasus Teluk Jakarta. Jurnal Teknik ITS, 9(1), 23–30. https://doi.org/10.12962/j23373539.v9i1.50609
Dagne, G. A., & Huang, Y. (2022). Bayesian Semiparametric Mixture Tobit Models with Left- Censoring, Skewness and Covariate Measurement Errors. BMC Cancer, 23(1), 1–7. https://doi.org/10.1002/sim.5799.Bayesian
Elgendy, A. R., El, A., El, M. S., Sawy, M. A. El, Alprol, A. E., & Zaghloul, G. Y. (2024). A comparative study of the risk assessment and heavy metal contamination of coastal sediments in the Red sea , Egypt , between the cities of El ‑ Quseir and Safaga. Geochemical Transactions, 25(3), 1–23. https://doi.org/10.1186/s12932-024-00086-8
Fahlevi, M. R., Bayhaqi, A., Sugianto, D. N., Fadli, M., Wang, H., Susanto, R. D., & Wouthuyzen, S. (2022). Karakteristik Massa Air di Selat Sunda dan Perairan Lepasnya. Buletin Oseanografi Marina, 11(3), 231–247. https://doi.org/10.14710/buloma.v11i2.41323
Gelman, A., Carlin, J. B., Stern, H. S., Dunson, D. B., Vehtari, A., & Rubin, D. B. (2013). Bayesian Data Analysis (Third). Chapman and Hall/CRC. https://doi.org/10.1201/b16018
Gelman, A., Simpson, D., & Betancourt, M. (2017). The Prior Can Often Only Be Understood in the Context of the Likelihood. Entropy, 19(555), 1–13. https://doi.org/10.3390/e19100555
George, B. J., Gains-germain, L., Broms, K., Black, K., Hays, M. D., Thomas, K. W., & Simmons, J. E. (2021). Censoring trace-level environmental data: statistical analysis considerations to limit bias. Environmental Science & Technology, 55(6), 3786–3795. https://doi.org/10.1021/acs.est.0c02256.Censoring
Giovanni, N.-G. S. D. and I. S. (2025). Average Total Precipitation from Days. https://giovanni.gsfc.nasa.gov/giovanni/
Haeruddin, Widowati, I., Rahman, A., Rumanti, M., & Iryanthony, S. B. (2021). Bioconcentration of lead (Pb) and cadmium (cd) in green-lipped mussels (perna viridis) in the coastal waters of semarang bay, indonesia. AACL Bioflux, 14(3), 1581–1595. https://bioflux.com.ro/docs/2021.1581-1595.pdf
Huynh, T., Ramachandran, G., Banerjee, S., Monteiro, J., Stenzel, M., Sandler, D. P., Engel, L. S., Kwok, R. K., Blair, A., & Stewart, P. A. (2014). Comparison of Methods for Analyzing Left- Censored Occupational Exposure Data. Ann. Occup. Hyg., 58(9), 1126–1142. https://doi.org/10.1093/annhyg/meu067
Iqbal, M., Denhi, A. D. A., Kristianto, & Prayoga, A. (2023). Morphological Analysis of Anak Krakatau Volcano after 22 December 2018 Eruption using Differential Interferometry Synthetic Aperture Radar (DInSAR). Journal of Geoscience, Engineering, Environment, and Technology, 8(2), 90–98. https://doi.org/10.25299/jgeet.2023.8.2.11651
Kartini, N., Boer, M., & Affandi, R. (2017). Pola Rekrutmen, Mortalitas, dan Laju Eksploitasi Ikan Lemuru (Amblygaster sirm, Walbaum 1792) di Perairan Selat Sunda. Biospecies, 10(1), 11–16. https://doi.org/10.22437/biospecies.v10i1.3483
Kementerian Lingkungan Hidup. (2025). Sistem Informasi Pelaporan Elektronik Lingkungan Hidup. https://simpel.menlhk.go.id/2023/pemda/evaluasi
Lemoine, N. P. (2019). Moving beyond noninformative priors: why and how to choose weakly informative priors in Bayesian analyses. Oikos, 128, 912–928. https://doi.org/10.1111/oik.05985
Lestari, D. A., Anzani, L., Zamil, A. S., Prasetyo, A., Simbolon, E. F., & Apriansyah, M. R. (2020). Pengaruh Gunung Laut Anak Krakatau Terhadap Pertumbuhan Rumput Laut di Selat Sunda. Jurnal Kemaritiman : Indonesian Journal of Maritime, 1(2), 75–88. https://doi.org/10.17509/ijom.v1i2.25590
Li, S., Wei, Z., Susanto, R. D., Zhu, Y., Setiawan, A., Xu, T., Fan, B., Agustiadi, T., Trenggono, M., & Fang, G. (2018). Observations of intraseasonal variability in the Sunda Strait throughflow. Journal of Oceanography, 74(5), 541–547. https://doi.org/10.1007/s10872-018-0476-y
Liu, S., Shi, J., Wang, J., Dai, Y., Li, H., Li, J., Liu, X., Chen, X., Wang, Z., & Zhang, P. (2021). Interactions Between Microplastics and Heavy Metals in Aquatic Environments: A Review. Frontiers in Microbiology, 12(April), 1–14. https://doi.org/10.3389/fmicb.2021.652520
Ma, Z., Li, H., Ye, Z., Wen, J., Hu, Y., & Liu, Y. (2020). Application of modified water quality index (WQI) in the assessment of coastal water quality in main aquaculture areas of Dalian, China. Marine Pollution Bulletin, 157(May), 1–8. https://doi.org/10.1016/j.marpolbul.2020.111285
McElreath, R. (2020). Statistical Rethinking - A Bayesian Course with Examples in R and Stan (Second). CRC Press. https://doi.org/10.1201/9780429029608
Munandar, E., Susanto, A., Nurdin, H. S., Syafrie, H., Hamzah, A., Khalifa, M. A., Budiaji, W., Febrio, E. P., & Dewi, I. Y. (2022). Dynamics of Coral Reefs Condition Before and After Sunda Strait Tsunami in Badul Island. Jurnal Perikanan Dan Kelautan, 12, 221–229. http://dx.doi.org/10.33512/jpk.v12i2.17423
Nugroho, T. M., Hartoko, A., & Suryanti. (2024). Analysis Of Mangrove Damage Before and After Tsunami in Sangiang Island Based on NDVI. Journal of Marquares, 11(1), 65–71. https://doi.org/10.14710/marj.v11i1.30111
Nurfajriah, U., Ijonu, S., Nyoman, I. G., Jaya, M., & Arisanti, R. (2024). Spatially Varying Regression Coefficient Model For Predicting Stunting Hotspots In Indonesia. Journal of Research in Science Education, 10(10), 7748–7755. https://doi.org/10.29303/jppipa.v10i10.8270
Penyelenggaraan Perlindungan Dan Pengeolaan Lingkungan Hidup, Pub. L. No. 22, VIII Kementrian Sekretarian Negara Republik Indonesia, 483 (2021). http://www.jdih.setjen.kemendagri.go.id/
Ramazanova, E., Bahetnur, Y., Yessenbayeva, K., Lee, S. H., & Lee, W. (2022). Spatiotemporal evaluation of water quality and risk assessment of heavy metals in the northern Caspian Sea bounded by Kazakhstan. Marine Pollution Bulletin, 181(113879), 1–10. https://doi.org/10.1016/j.marpolbul.2022.113879
Ravenzwaaij, D. Van, Cassey, P., & Brown, S. D. (2018). A simple introduction to Markov Chain Monte – Carlo sampling. Psychon Bull Rev, 25, 143–154. https://doi.org/10.3758/s13423-016-1015-8
Ristanto, D., Ambariyanto, A., & Yulianto, B. (2021). Water Quality Assessment Based on National Sanitations Foundation Water Quality Index during Rainy Season in Sibelis and Kemiri Estuaries Tegal City. IOP Conference Series: Earth and Environmental Science, 750(012013), 1–10. https://doi.org/10.1088/1755-1315/750/1/012013
Röver, C., Schmidli, H., Schmid, C. H., Weber, S., & Friede, T. (2021). On weakly informative prior distributions for the heterogeneity parameter in Bayesian random-effects meta- analysis. Research Synthesis Methods, 12, 448–474. https://doi.org/10.1002/jrsm.1475
Safford, H., Zuniga-montanez, R. E., Kim, M., Wu, X., Wei, L., Sharpnack, J., Shapiro, K., & Bischel, H. N. (2022). Wastewater-Based Epidemiology for COVID-19: Handling qPCR Nondetects and Comparing Spatially Granular Wastewater and Clinical Data Trends. ACS EST Water, 2, 2114–2124. https://doi.org/10.1021/acsestwater.2c00053
Sobaruddin, D. P., Armawi, A., & Martono, E. (2017). Model Traffic Separation Scheme (TSS) Di Alur Laut Kepulauan Indonesia (AlKI) I Di Selat Sunda Dalam Mewujudkan Ketahanan Wilayah. Jurnal Ketahanan Nasional, 23(1), 104. https://doi.org/10.22146/jkn.22070
Subekti, S., Amiin, M. K., Ardiyanti, H. B., Yudarana, M. A., Achmadi, I., & Akbar, R. E. K. (2021). Molecular epidemiology of helminth diseases of the humpback grouper , Cromileptes altivelis , as a pattern for mapping fish diseases in the. Veterinary World, 14(5), 1324–1329. https://www.doi.org/10.14202/vetworld.2021.1324-1329
Susanto, A., Nurdin, H. S., Khalifa, M. A., Munandar, E., Syafrie, H., Alansar, T., Sulistyono, B., & Raihan, A. (2023). Sunda Strait Coastal Management with Mangrove Planting as an Effort for Mitigation of Disaster and Climate Change (Blue Carbon). Journal of Maritime Empowerment, 5(2), 48–55. https://doi.org/10.31629/jme.v5i2.5711
Tolkou, A. K., Toubanaki, D. K., & Kyzas, G. Z. (2023). Detection of Arsenic, Chromium, Cadmium, Lead, and Mercury in Fish: Effects on the Sustainable and Healthy Development of Aquatic Life and Human Consumers. Sustainability (Switzerland), 15(23), 1–17. https://doi.org/10.3390/su152316242
Uddin, M. G., Nash, S., & Olbert, A. I. (2021). A review of water quality index models and their use for assessing surface water quality. Ecological Indicators, 122(107218), 1–21. https://doi.org/10.1016/j.ecolind.2020.107218
Wood, M. D., Beresford, N. A., & Copplestone, D. (2011). Limit of detection values in data analysis: Do they matter? Radioprotection, 46(6 SUPPL.), 85–90. https://doi.org/10.1051/radiopro/20116728s
Yonvitner, Y., LIoret, J., Boer, M., Kurnia, R., Akmal, S. G., Yuliana, E., Yani, D. E., Gómez, S., & Setijorini, L. E. (2020). Vulnerability of marine resources to small-scale fishing in a tropical area: The example of Sunda Strait in Indonesia. Fisheries Management and Ecology, 27(5), 472–480. https://doi.org/10.1111/fme.12428
License
Copyright (c) 2026 Iis Afrianti, Sjaifuddin Sjaifuddin, Najmi Firdaus

This work is licensed under a Creative Commons Attribution 4.0 International License.
Authors who publish with Jurnal Penelitian Pendidikan IPA, agree to the following terms:
- Authors retain copyright and grant the journal right of first publication with the work simultaneously licensed under a Creative Commons Attribution 4.0 International License (CC-BY License). This license allows authors to use all articles, data sets, graphics, and appendices in data mining applications, search engines, web sites, blogs, and other platforms by providing an appropriate reference. The journal allows the author(s) to hold the copyright without restrictions and will retain publishing rights without restrictions.
- Authors are able to enter into separate, additional contractual arrangements for the non-exclusive distribution of the journal's published version of the work (e.g., post it to an institutional repository or publish it in a book), with an acknowledgment of its initial publication in Jurnal Penelitian Pendidikan IPA.
- Authors are permitted and encouraged to post their work online (e.g., in institutional repositories or on their website) prior to and during the submission process, as it can lead to productive exchanges, as well as earlier and greater citation of published work (See The Effect of Open Access).






