Spatial Extreme Value With Bayesian Hierarchical Model (Studi Kasus: Pemodelan Curah Hujan Ekstrem Di Kabupaten Ngawi)

Hazhiah, Indria Tsani (2016) Spatial Extreme Value With Bayesian Hierarchical Model (Studi Kasus: Pemodelan Curah Hujan Ekstrem Di Kabupaten Ngawi). Masters thesis, Institut Technology Sepuluh Nopember.

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Abstract

Ekstrem Curah hujan ekstrem merupakan fenomena alam yang langka sehingga tergolong salah satu iklim ekstrem yang dapat memicu bencana alam seperti banjir dan longsor. Bencana tersebut menjadi penyebab keresahan masyarakat dan menimbulkan berbagai penyakit pada masyarakat di wilayah tersebut sehingga perlu adanya identifikasi curah hujan ekstrem untuk mengurangi dampak negatif yang ditimbulkan. Extreme value theory (EVT) adalah salah satu metode statistika yang digunakan untuk mempelajari perilaku-perilaku nilai-nilai ekstrem. Salah satu yang dihitung dalam EVT adalah return level yaitu suatu level ( kuantil dengan peluang 1/T) kejadian ekstrem yang diharapkan terlampaui dalam periode T. Sebelum menentukan nilai return level, terlebih dahulu harus diketahui parameter distribusi EVT yang dipilih dengan menggunakan data yang banyak. Namun kenyataannya peristiwa curah hujan ekstrem jarang terjadi sehingga data pengamatan jumlahnya terbatas yang digunakan dalam penaksiran parameter. Salah satu metode yang diharapkan dapat mengatasi jumlah data pengamatan yang terbatas adalah Bayesian. Keunggulan Bayesian salah satunya adalah dapat melakukan updating informasi terhadap likelihood melalui distribusi prior karena informasi pada likelihood terbatas apabila data pengamatan sedikit. Selain itu, informasi geografi dan klimatologi yang tidak bisa diakomodasi secara penuh dalam model diharapkan dapat ditangkap oleh struktur spasial pada Bayesian Hierarchical Model (BHM). Penelitian ini menganalisis data curah hujan ekstrem di Kabupaten Ngawi, Jawa Timur dengan pendekatan BHM pada Generalized Pareto Distribution (GPD) yang merupakan distribusi asimtotis dari Peak Over Threshold (POT). Pada penelitian ini dengan menggunakan BHM menghasilkan return level yang lebih baik dilihat dari SE yang terkecil dibandingkan dengan hanya menggunakan POT. ============================================================================================================ Extreme precipitation is a rare natural phenomenon that classified as one of extreme climates. It could lead to natural disasters such as floods and landslides which cause public unrest and inflict various diseases in the region thus need to identify the extreme precipitation in order to reduce the negative impact of the causes it. Extreme value theory (EVT) is one of statistical models that used to learn the behaviors of extreme values. The one of the counted in the extreme value theory is return level. Return level is maximum value the future periods that informs time scales incident of the next extreme precipitation else. The first that should know is parameter of distribution estimation in extreme value theory that be chosen by using many data before be determine the value of return level. The actually extreme precipitation events are rare thus we just have few amount of observational data that used in the valuation of parameters. One of the models that hope coping limited amount of observational data is Bayesian. One of the Bayesian advantage could be updating of information on the likelihood through the information on the prior distribution because the limited information obtained from the likelihood if only using a small data. Coley (2007) states that the extreme values at different locations are influenced by factors of geography and climatology. Factors Geography and climatology could not be accommodated fully in the model of these deficiencies was captured by the spatial structure of Bayesian hierarchical models. This paper analyzed data extreme precipitation in Ngawi regency of East Java with the approach of the Bayesian hierarchical model (BHM) on Generalized Pareto Distribution which a asimtotis distribution of peak over thershold (POT) methods. The results of this research showed that BHM be able cope a limited amount of observational data and Factors Geography and climatology that could not be accommodated fully in the model. This is shown in the result data using BHM that has Square Error (SE) of return level smaller than without using the BHM. BHM approach applied on generalized Pareto distribution which is asimtotis of POT.

Item Type: Thesis (Masters)
Additional Information: RTSt 519.542 Haz s
Uncontrolled Keywords: Curah Hujan, EVT, Peaks Over Threshold, Generalized Pareto Distribution, Return Level, Bayesian hierarchical model
Subjects: Q Science > QA Mathematics > QA279.5 Bayesian statistical decision theory.
Divisions: Faculty of Mathematics and Science > Statistics > 49101-(S2) Master Thesis
Depositing User: Mr. Tondo Indra Nyata
Date Deposited: 22 Jan 2020 08:01
Last Modified: 22 Jan 2020 08:01
URI: http://repository.its.ac.id/id/eprint/72902

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