Murniati, Tri (2020) Pendekatan Bayesian pada Model Regresi Mixture Poisson untuk Estimasi Fungsi Intensitas Spatial Point Process (Studi Kasus Pola Titik Persebaran Fasilitas Kesehatan Tingkat Pertama di Surabaya). Masters thesis, Institut Teknologi Sepuluh Nopember.
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Abstract
Spatial point process sangat berguna sebagai model statistika untuk menganalisa pengamatan point pattern dimana titik (point) menunjukkan lokasi objek penelitian. Point pattern dapat dilihat sebagai proses Poisson jika diasumsikan antara titik lokasi saling independen yang kemudian disebut sebagai Poisson Point Process. Intensitas sebagai momen pertama Poisson Point Process didefinisikan sebagai rasio jumlah titik per unit area. Fungsi intensitas dapat dipandang sebagai model loglinier Poisson Point Process atau regresi Poisson. Pada kondisi dimana proses Poisson memiliki intensitas yang bervariasi secara spasial (Nonhomogeneus Poisson Process), regresi mixture Poisson dapat digunakan untuk pemodelan intensitas karena pemodelan dilakukan pada proses Poisson yang dibedakan menjadi k komponen terbatas yang saling heterogen. Untuk melakukan estimasi parameter regresi mixture dibentuk fungsi likelihood yang komplek sehingga pendekatan Bayesian dengan Markov Chain Monte Carlo (MCMC) sering digunakan. Pada penelitian ini pendekatan Bayesian pada model regresi mixture Poisson diterapkan untuk memperoleh model intensitas titik lokasi fasilitas kesehatan tingkat pertama (FKTP) di Surabaya. Intensitas FKTP dapat digunakan untuk mengukur pemerataan fasilitas kesehatan yang menjadi perhatian Dinas Kesehatan guna memenuhi kebutuhan dasar kesehatan. Analisis menggunakan grid dengan ukuran irregular tessellation sesuai dengan batas kecamatan diplotkan pada peta Surabaya. Variabel kovariat yang berkaitan dengan tingkat kebutuhan layanan kesehatan digambarkan dengan kepadatan penduduk dan persentase rumah tangga perilaku hidup bersih sehat serta aksesibilitas yang digambarkan dengan angka keterkaitan dan panjang jalan dalam kondisi baik, mencerminkan karakteristik masing-masing kecamatan. Analisis menunjukkan bahwa persebaran FKTP di Surabaya memiliki intensitas yang Nonhomogeneous Poisson Process dengan dua kategori mixture. Persebaran FKTP secara signifikan dipengaruhi oleh tingkat kebutuhan layanan kesehatan dan aksesibilitas kecamatan.
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Spatial point process is statistical model for analyzing point patterns where points indicate the location of research objects. A point pattern can be seen as a Poisson process if it is assumed that between points of location are mutually independent. It is referred as the Poisson Point Process. Intensity as the first moment of the Poisson Point Process is defined as the ratio of the number of points per unit area. The intensity function can be seen as a loglinear Poisson Point Process or Poisson regression model. Under conditions where the Poisson process has a spatially varying intensity (Nonhomogeneus Poisson Process), Poisson mixture regression can be used for intensity modeling because it is done on the Poisson process which is divided into k-th heterogeneous components. To estimate the mixture regression parameters a complex likelihood function is formed so that the Bayesian approach with Markov Chain Monte Carlo (MCMC) is popular. In this study the Bayesian approach to the mixture Poisson regression model was applied to obtain the point intensity model of the location of the primary health centres (PHC) in Surabaya. Intensity of PHC can be used to measure the distribution of health facilities that are the Health Office concern to meet basic health needs. The analysis uses a grid with irregular tessellation size in accordance with the subdistrict boundaries plotted on the Surabaya map. Covariate variables related to the level of need for health services are depicted by population density and percentage of households with healthy hygiene behavior and accessibility as illustrated by the linkage rate and road length in good condition reflecting the characteristics of each district. The analysis shows that PHC distribution in Surabaya follows Nonhomogeneous Poisson Process with two categories of mixture. The distribution of PHC is significantly influenced by the level of health service needs and the accessibility of sub-districts.
| Item Type: | Thesis (Masters) |
|---|---|
| Additional Information: | RTSt 519.542 Tri p-1 |
| Uncontrolled Keywords: | Poisson Point Process, Regresi Mixture Poisson, Analisis Bayesian, Intensitas FKTP |
| Subjects: | G Geography. Anthropology. Recreation > G Geography (General) > G70.212 ArcGIS. Geographic information systems. G Geography. Anthropology. Recreation > G Geography (General) > G70.217 Geospatial data Q Science > QA Mathematics > QA274.2 Stochastic analysis Q Science > QA Mathematics > QA278.2 Regression Analysis. Logistic regression Q Science > QA Mathematics > QA279.5 Bayesian statistical decision theory. |
| Divisions: | Faculty of Science and Data Analytics (SCIENTICS) > Statistics > 49101-(S2) Master Thesis |
| Depositing User: | Tri Murniati |
| Date Deposited: | 13 Mar 2025 07:04 |
| Last Modified: | 13 Mar 2025 07:04 |
| URI: | http://repository.its.ac.id/id/eprint/74694 |
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