Estimasi Parameter Pada Model Neyman Scott Cox Process (NSCP) Menggunakan Convolutional Neural Network (CNN)

Erlinda, Relly (2025) Estimasi Parameter Pada Model Neyman Scott Cox Process (NSCP) Menggunakan Convolutional Neural Network (CNN). Masters thesis, Institut Teknologi Sepuluh Nopember.

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Abstract

Spatial point process digunakan untuk menganalisis distribusi lokasi objek di suatu ruang geografis, seperti episentrum gempa bumi. Model Neyman Scott Cox Process (NSCP) merupakan salah satu model yang dapat menganalisis data spasial titik yang memiliki pola cluster. Bentuk likelihood model NSCP sulit dievaluasi secara analitik, maka estimasi parameter dapat dilakukan menggunakan metode seperti Composite likelihood Estimation dan Minimum contrast. Seiring perkembangan dalam bidang neural network, pendekatan ini menawarkan potensi besar untuk estimasi parameter. Neural network mampu memodelkan hubungan non linier antar titik dalam ruang tanpa memerlukan asumsi eksplisit mengenai ketergantungan spasial. C onvolutional Neural Network (CNN) telah terbukti efektif dalam berbagai aplikasi khususnya untuk analisis citra. Akan tetapi, penerapannya dalan analisis spatial point process masih terbatas. Penelitian ini mengkaji CNN untuk estimasi parameter model NSCP dengan melibatkan variabel kovariat. Model tersebut dievaluasi melalui studi simulasi dengan mambangkitkan data point pattern berdasarkan berbagai kombinasi parameter model NSCP, serta diterapkan pada data gempa bumi di wilayah Sulawesi dan Maluku. Hasil penelitian menunjukkan bahwa CNN model 1 memberikan performa pelatihan stabil tanpa indikasi overfitting, ditunjukkan oleh kesesuaian antara loss pelatihan dan validasi serta menghasilkan estimasi parameter yang paling akurat dan konsisten dibanding metode lainnya. Model CNN model 2 menghasilkan estimasi mendekati composite likelihood, dimana interpretasi pengaruh kovariatnya belum sepenuhnya stabil. Sementara composite likelihood dan minimum contrast menghasilkan intensitas yang menyebar secara global, sehingga berisiko memberikan estimasi berlebih di luar pusat klaster. Meskipun demikian, ketiga pendekatan secara umum menunjukkan pola dengan zona risiko tinggi di wilayah utara Sulawesi, Maluku, seperti Manado, Ternate dan Laut Banda di selatan Pulau Seram.
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Spatial point process is used to analyze the distribution of objects locations in a geographic space, such as the earthquake epicenters. The Neyman Scott Cox Process (NSCP) model is one model that can analyze spatial point data that has a clusters pattern. The likelihood function of NSCP model is difficult to evaluate analytically, so parameter estimation can be performed using methods such as Composite likelihood Estimation and Minimum contrast. However, along with developments in neural networks, this approach offers great potential for parameter estimation. Neural networks are able to model nonlinear relationships between points in space without requiring explicit assumptions about spatial dependence. Convolutional Neural Networks (CNN) has proven to be effective in various applications, especially for image analysis. However, its application in spatial point process analysis is still limited. This study explores CNN to estimate parameters for the NSCP model with several covariates. The model was evaluated through a simulation study by generating point patterns based on various combinations of NSCP model parameters, and applied to earthquake data in the Sulawesi and Maluku regions. The results show that CNN model 1 provides stable training performance with no indication of overfitting, indicated by the agreement between training and validation loss and produces the most accurate and consistent parameter estimates compared to other methods. The CNN model 2 produces estimates close to the composite likelihood, but the interpretation of the covariate effect is not fully stable. Meanwhile, composite likelihood and minimum contrast produce globally spread intensities, thus risking overestimation outside the cluster center. However, the three approaches generally show patterns with high risk zones in the northern regions of Sulawesi, Maluku, such as Manado, Ternate and Banda Sea in the south of Seram island.

Item Type:	Thesis (Masters)
Uncontrolled Keywords:	Convolutional Neural Network, Estimasi parameter, Neural Network, NSCP, Spatial Point Process, Parameter Estimation
Subjects:	Q Science > QA Mathematics > QA278.55 Cluster analysis Q Science > QA Mathematics > QA76.87 Neural networks (Computer Science)
Divisions:	Faculty of Science and Data Analytics (SCIENTICS) > Statistics > 49101-(S2) Master Thesis
Depositing User:	Relly Erlinda
Date Deposited:	05 Aug 2025 11:59
Last Modified:	05 Aug 2025 11:59
URI:	http://repository.its.ac.id/id/eprint/127550

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