Estimasi Parameter Pada Model Cauchy Cluster Process Berbasis Regresi Logistik Dengan Regularisasi Elastic Net (Studi Kasus: Kejadian Gempa Bumi Di Sumatra)

Chintyana, Alissa (2023) Estimasi Parameter Pada Model Cauchy Cluster Process Berbasis Regresi Logistik Dengan Regularisasi Elastic Net (Studi Kasus: Kejadian Gempa Bumi Di Sumatra). Masters thesis, Institut Teknologi Sepuluh Nopember.

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Abstract

Cox point process umumnya digunakan untuk pemodelan kejadian yang mengandung unsur cluster, seperti kejadian gempa bumi. Inhomogeneous Cox point process adalah salah satu model populer untuk analisis kejadian gempa bumi yang melibatkan kovariat geologis. Namun demikian, prosedur two-step estimation tidak dapat berjalan dengan baik ketika terdapat korelasi tinggi antar kovariat. Regularisasi elastic net merupakan metode yang umum digunakan dalam penanganan multikolinieritas. Estimasi berbasis regresi logistik dipertimbangkan untuk digunakan dengan harapan dapat mengurangi root-mean-square error (RMSE). Dalam penelitian ini, two-step estimation diadopsi dengan penyelesaian persamaan regularisasi menggunakan Coordinate Descent Algorithm. Metode yang diusulkan diterapkan pada model Cauchy cluster process yang merupakan salah satu bentuk khusus dari Neyman-Scott Cox process. Studi simulasi dijalankan dengan mempertimbangkan tiga metode regularisasi yaitu ridge (α=0), elastic net (α=0,5), dan lasso (α=1). Berdasarkan nilai maximum second-order composite likelihood dan RMSE, ridge diperhitungkan untuk digunakan ketika terdapat kovariat berkorelasi dan point pattern dengan cluster kuat. Model terbaik untuk pemodelan gempa bumi di Sumatra ditentukan berdasarkan nilai maximum second-order composite likelihood terbesar. Cauchy cluster process berbasis regresi logistik dengan regularisasi ridge merupakan model terbaik. Berdasarkan model terbaik, kovariat geologis dengan pengaruh terbesar terhadap risiko gempa bumi di Sumatra adalah zona subduksi. Risiko gempa bumi di Sumatra diprediksi tinggi di bagian utara dan barat Pulau Sumatra yang berbatasan dengan Samudra Hindia.
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The Cox point process is generally used for modeling natural disasters, such as earthquakes. The inhomogeneous Cox point process is one of the popular models for the analysis of earthquake events involving geological variables. However, the standard two-step estimation procedure does not work well when the variables show a high correlation. Ridge regularization has a reputation for dealing with multicollinearity problems. In this study, two-step estimation was adopted by adding ridge regularization for the Cox point process model using the Coordinate Descent Algorithm. Logistic regression-based estimates were considered for use in the hope of reducing bias. The proposed method is applied to model the distribution of earthquakes in Sumatra with the Cauchy cluster process. Simulation studies were carried out considering three regularization methods: ridge (α=0), elastic net (α=0.5) and lasso (α=1). Based on the maximum second-order composite likelihood and RMSE values, ridge is better used if there are correlated covariates and point patterns with strong clusters. The best model for earthquake modeling in Sumatra is determined based on the highest maximum second-order composite likelihood value. Cauchy cluster process based on logistic regression with ridge regularization is the best model. Based on the best model, the geological covariate with the greatest influence on earthquake risk in Sumatra is the subduction zone. The risk of earthquakes in Sumatra is predicted to be high in the northern and western parts of Sumatra Island, which are bordered by the Indian Ocean.

Item Type:	Thesis (Masters)
Uncontrolled Keywords:	earthquake, multicollinearity, point process, ridge regularization, elastic net, gempa bumi, multikolinieritas, regularisasi ridge
Subjects:	H Social Sciences > HA Statistics > HA29 Theory and method of social science statistics Q Science > QA Mathematics > QA275 Theory of errors. Least squares. Including statistical inference. Error analysis (Mathematics) Q Science > QA Mathematics > QA278.2 Regression Analysis. Logistic regression
Divisions:	Faculty of Science and Data Analytics (SCIENTICS) > Statistics > 49101-(S2) Master Thesis
Depositing User:	Alissa Chintyana
Date Deposited:	17 Feb 2023 03:47
Last Modified:	17 Feb 2023 03:47
URI:	http://repository.its.ac.id/id/eprint/97557

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