Pemodelan Pengamatan Ekstrem Spasial Non Stationer Menggunakan Bayesian Hierarki

., Amran (2015) Pemodelan Pengamatan Ekstrem Spasial Non Stationer Menggunakan Bayesian Hierarki. Doctoral thesis, Institut Teknologi Sepuluh Nopember.

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Abstract

Masalah utama yang dibahas dalam disertasi ini ialah pemodelan pengamatan ekstrem berdasarkan Teorema Nilai Ekstrem (TNE) menggunakan Model Bayesian Hierarki Spasial Non Stasioner Regional (MBHSNSR) yang menjadi temuan baru dalam disertasi ini dan diaplikasikan pada data curah hujan. Prediksi curah hujan ekstrem melalui Return Level (RL) sangat dibutuhkan untuk mengurangi atau mencegah dampak negatif dari curah hujan ekstrem dan juga untuk menyusun rencana pembangunan yang efisien. Dalam implementasinya, pemodelan pengamatan ekstrem menghadapi kendala berupa keterbatasan jumlah pengamatan ekstrem dan masalah non stasioneritas daerah pengamatan. MBHSNSR ditujukan untuk mengatasi masalah terbatasnya jumlah pengamatan berdasarkan sifat non stasioneritas proses spasial daerah pengamatan. Nilai RL yang dihitung menggunakan MBHSNSR berdasarkan model yang dikonstruksi dengan mengintegrasikan model Bayesian hierarki dan metode penaksiran regional. Model Bayesian Hierarki digunakan untuk mengakomodasi uncertainty pada pengukuran data curah hujan, pada proses spasial yang mengendalikan pola curah hujan ekstrem, dan parameter. Metode penaksiran regional digunakan untuk mengatasi masalah keterbatasan jumlah data. Dalam studi tentang curah hujan ekstrem di daerah pengamatan non stasioner, proses inferensi dilakukan melalui partisi daerah pengamatan menjadi kluster stasioner. Penelitian ini mengembangkan suatu metode partisi melalui identifikasi dan karakterisasi distribusi curah hujan ekstrem menggunakan statistik Silhouette dan algoritma k-mean. Hasil identifikasi dan karakterisasi ini menghasikan kluster stasioner dengan fungsi distribusi yang serupa. Berdasarkan kompleksitas distribusi curah hujan ekstrem di setiap kluster, MBHSNSR diuraikan dalam tiga tahap yaitu tahap pemodelan data, tahap pemodelan proses, dan tahap pemilihan distribusi prior. MBHSNSR menggunakan data regional yang diperoleh di setiap kluster melalui suatu fungsi transformasi. Implementasi MBHSNSR pada data curah hujan harian di dua puluh delapan stasiun curah hujan periode lima belas tahun di Kabupaten Malang menunjukkan hasil penaksiran RL dengan tingkat akurasi yang lebih baik. Besarnya prosentase reduksi variansi melalui pendekatan regional yakni 32,63% sampai dengan 83,63% dengan rata-rata prosentase reduksi sebesar 61,84%. Selain itu, pemodelan spasial parameter distribusi TNE menggunakan MBHSNSR menunjukkan hasil yang lebih baik dari model independen dan model pooled berdasarkan nilai Deviance Information Criterion (DIC) terkecil. Nilai DIC untuk MBHSNSR sebesar 5503,8. Nilai DIC untuk model independen sebesar 6147,2 dan model pooled sebesar 5887,0. Dalam rangka mencegah dampak negatif kejadian ekstrem, MBHSNSR dapat dipertimbangkan sebagai suatu bagian dari upaya mitigasi khususnya untuk prediksi RL. =========================================================================================== The main problem discussed in this research is the modeling of extreme observations based on Extreme Value Theorem (EVT) using Hierarchical Bayesian Model of Spatial Non Stationary Region (MBHSNSR) which became the new findings in this research and applied to precipitation data. Prediction of extreme rainfall through the Return Level (RL) is needed to reduce or prevent the negative impact of extreme rainfall and also for an efficient development plan. Problems of extreme observations modeling are a limited number of extreme observations and non stationary spatial process of observation area. MBHSNSR intended to overcome the limited number of observations based on the non stationary spatial process of observation area. RL values were calculated using MBHSNSR based on a model constructed by integrating Hierarchical Bayesian models and methods of the regional estimation. Hierarchical Bayesian models used to accommodate uncertainty in the measurement of rainfall data, the processes that control the spatial patterns of extreme rainfalls, and parameters. Regional estimation method used to overcome the problem of limited number of data. In the study of extreme rainfall in the area of non stationary spatial process, inference process is done through the partition into clusters stationary observation area. This study develops a method of partitioning through the identification and characterization of the distribution of extreme rainfalls using Silhouette statistics and k-means algorithm. The identification and characterization process produce stationary clusters with similar distribution function. Based on the complexity of extreme rainfall distribution on each cluster, MBHSNSR described in three stages: data modeling, process modeling and prior distribution stage. MBHSNSR using regional data obtained on each cluster through a transformation function. Implementation MBHSNSR on daily rainfall data at twenty eight stations rainfall for fifteen years period in Malang shows the results of the estimation of the RL with better accuracy. Variance reduction through a regional approach is 32.63% to 83.63% with an average percentage reduction of 61.84%. In addition, modeling distribution parameters using MBHSNSR showed better results than independent models and pooled model based on the smallest Deviance Information Criterion (DIC) value. DIC value for MBHSNSR is 5503,8. DIC value for independent model is 6147,2 and DIC value for pooled model is 5887,0. In order to avoid negative impact of extreme events, MBHSNSR can be considered as a part of the mitigation effort especially for RL prediction.

Item Type: Thesis (Doctoral)
Additional Information: RDSt 519.542 Amr p
Uncontrolled Keywords: Extreme value theorem, Hierarchical bayesian model, Non stationary spatial process, Return level, Silhouette statistics, k-mean algorithm, Teorema nilai ekstrem, Proses spasial non stasioner
Subjects: H Social Sciences > HA Statistics
Q Science > QA Mathematics > QA279.5 Bayesian statistical decision theory.
Divisions: Faculty of Mathematics and Science > Statistics > (S3) PhD Theses
Depositing User: Eny Widiastuti -
Date Deposited: 09 Apr 2018 08:14
Last Modified: 09 Apr 2018 08:14
URI: http://repository.its.ac.id/id/eprint/51717

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