Febritasari, Popy (2019) Model Glarma Binomial Negatif Dengan Pendugaan Algoritma Metropolis Hasting-Kalman Filter (Studi Kasus Banyaknya Kejadian Kecelakaan Lalu Lintas Kategori Berat Di Wilayah Hukum Polres “X”). Magister thesis, Universitas Brawijaya.
Abstract
Data univariat time series yang berdistribusi poisson dengan kasus overdispersi di modelkan menggunakan analisis Generalized Linear Autoregressive Moving Average (GLARMA) Binomial Negatif. Analisis pendugaan parameter menggunakan Algoritma Metropolis Hasting-Kalman Filter. Algoritma Metropolis Hasting didasarkan pada distribusi beta sebagai distribusi prior konjugat dan distribusi posterior dari perkalian distribusi prior dengan fungsi likelihood binomial negatif. Pendugaan parameter menggunakan Algoritma Kalman Filter menggunakan serangkaian pengukuran pengamatan dari waktu ke waktu, mengandung noise statistik, dan menghasilkan estimasi parameter yang tidak diketahui menggunakan perkiraan distribusi probabilitas bersama sehingga menghasilkan pendugaan yang sesuai dengan meminimalkan mean square error (MSE). Penggunaan Algoritma Metropolis Hasting-Kalman Filter pada pendugaan model GLARMA Binomial Negatif menghasilkan MSE sebesar 0.6318947. Hasil MSE Algoritma Metropolis Hasting-Kalman Filter lebih kecil daripada Algoritma Metropolis Hasting, sehingga dapat disimpulkan bahwa Algoritma Kalman Filter mampu memperkecil MSE pada pendugaan model GLARMA Binomial Negatif.
English Abstract
Univariate time series in Poisson distribution with overdispersion cases were modeled using Generalized Linear Autoregressive Moving Average (GLARMA) Negative Binomial analysis. Parameter estimation analysis taken by Metropolis Hasting-Kalman Filter Algorithm. The Metropolis Hasting algorithm is based on the beta distribution as the prior conjugate distribution and the posterior distribution. Estimation of parameters using the Kalman Filter Algorithm uses a series of observational measurements over time, contains statistical noise, and results in the estimation of unknown parameters using a joint probability distribution estimate so as to produce a corresponding estimate by minimizing the mean square error (MSE). Metropolis Hasting-Kalman Filter Algorithm in the estimation of the Negative Binomial GLARMA model produces an MSE of 0.6318947. MSE of Metropolis Hasting-Kalman Filter Algorithm are smaller than the Metropolis Hasting Algorithm, so it can be concluded that the Kalman Filter Algorithm is able to minimize MSE in the estimation of the Negative Binomial GLARMA model.
Other obstract
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| Item Type: | Thesis (Magister) |
|---|---|
| Identification Number: | TES/518.1/FEB/m/2019/041911437 |
| Uncontrolled Keywords: | ALGORITHMS, KALMAN FILTERING--MATHEMATICAL MODELS, TIME-SERIES ANALYSIS |
| Subjects: | 500 Natural sciences and mathematics > 518 Numerical analysis > 518.1 Algorithms |
| Divisions: | S2/S3 > Magister Statistika, Fakultas MIPA |
| Depositing User: | Budi Wahyono Wahyono |
| Date Deposited: | 20 Jan 2020 01:48 |
| Last Modified: | 20 Jan 2020 01:48 |
| URI: | http://repository.ub.ac.id/id/eprint/178084 |
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