Inhomogeneous Log-Gaussian Cox Process dengan Piecewise Constant Covariate (Studi Kasus: Risiko Penyebaran COVID-19 di Jawa Timur)

Fadlurohman, Alwan (2023) Inhomogeneous Log-Gaussian Cox Process dengan Piecewise Constant Covariate (Studi Kasus: Risiko Penyebaran COVID-19 di Jawa Timur). Masters thesis, Institut Teknologi Sepuluh Nopember.

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Abstract

Inhomogeneous Log-Gaussian Cox Process (LGCP) merupakan salah satu model proses titik spasial yang fleksibel untuk memodelkan data pola titik spasial dengan pola agregasi. Salah satu hal utama dalam analisis Inhomogeneous LGCP adalah untuk mendapatkan fungsi intensitas yang bergantung pada kovariat spasial. Selama ini kovariat spasial yang digunakan untuk mengetahui distribusi spasial pada model LGCP adalah fungsi kontinu. Akan tetapi, tidak semua data tersedia dalam fungsi kontinu, misalnya seperti data official statistics yang dihimpun berdasarkan kewilayahan. Penelitian ini berfokus pada estimasi parameter model Inhomogeneous LGCP ketika kovariat yang digunakan adalah piecewise constant (kovariat berdasarkan kewilayahan). Hasil dari estimasi pada model Inhomogeneous LGCP dengan kovariat piecewise constant akan dibandingkan dengan estimasi parameter menggunakan pendekatan Berman-Turner yang mengasumsikan kovariat kontinu pada risiko penyebaran COVID-19 di Jawa Timur. Perbandingan kedua model akan di evaluasi dengan melihat plot envelope K-Function. Hasil visualisasi plot envelope K-Function menunjukkan bahwa model Inhomogeneous LGCP dengan kovariat piecewise constant cenderung memiliki performa yang lebih baik, serta menunjukkan pola agregasi yang lebih cluster karena menghasilkan estimasi parameter ψ yang lebih besar. Berdasarkan hasil tersebut, model Inhomogeneous LGCP dengan kovariat piecewise constant dapat dijadikan alternatif dari model proses titik spasial ketika terdapat data titik dan kovariat berupa piecewise constant. Kovariat spasial yang berpengaruh signifikan pada pemodelan risiko penyebaran kasus terkonfirmasi COVID-19 dengan Inhomogeneous LGCP adalah kepadatan penduduk, kepadatan penduduk berusia di atas 60 tahun, kepadatan industri besar dan sedang, dan kepadatan pasar.
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Inhomogeneous Log-Gaussian Cox Process (LGCP) is one of the spatial point process models that is flexible to modelling spatial point process data with aggregation patterns. One of the main concerns in Inhomogeneous LGCP analyzing is to obtain intensity functions that depend on spatial covariates. Currently, the spatial covariates used to determine the spatial distribution in the LGCP model are continuous functions. However, not all data are available in continuous functions, for example, such as official statistics data aggregated by region. This study focuses on estimating the parameters of the Inhomogeneous LGCP model when the covariates used are piecewise constant (covariates based on region). The results of the estimation of the Inhomogeneous LGCP model with piecewise constant covariates will be compared with parameter estimates using the Berman-Turner approach which assumes continuous covariates at the risk of spreading COVID-19 in East Java. Comparison of the two models will be evaluated by looking at the K-Function envelope plot. The visualization results of the K-Function envelope plot show that the Inhomogeneous LGCP model with piecewise constant covariates tends to have better performance, and shows a more cluster aggregation pattern because it produces a larger parameter estimate of ψ. Based on these results, the Inhomogeneous LGCP model with piecewise constant covariate can be used as an alternative to the spatial point process model when there are data points and covariates in the form of piecewise constant. Spatial covariates that have a significant effect on modelling the risk of spreading confirmed cases of COVID-19 with Inhomogeneous LGCP are population density, population density over 60 years old, large and medium industrial density, and market density.

Item Type:	Thesis (Masters)
Uncontrolled Keywords:	Kepadatan Kerumunan, Kovariat Spasial, K-Function, Proses titik spasial, Crowd Density, K-Function, Spatial Covariate, Spatial Point Process
Subjects:	H Social Sciences > HA Statistics
Divisions:	Faculty of Science and Data Analytics (SCIENTICS) > Statistics > 49101-(S2) Master Thesis
Depositing User:	Alwan Fadlurohman
Date Deposited:	28 Aug 2023 07:19
Last Modified:	28 Aug 2023 07:19
URI:	http://repository.its.ac.id/id/eprint/103434

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