BAYESIAN MODEL AVERAGING GAMMA DAN WEIBULL BERBASIS CAMPURAN HIERARKI TIGA TINGKAT UNTUK PREDIKSI CURAH HUJAN BULANAN DKI JAKARTA

ELVIN FERNANDO, . (2026) BAYESIAN MODEL AVERAGING GAMMA DAN WEIBULL BERBASIS CAMPURAN HIERARKI TIGA TINGKAT UNTUK PREDIKSI CURAH HUJAN BULANAN DKI JAKARTA. Sarjana thesis, UNIVERSITAS NEGERI JAKARTA.

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Abstract

Curah hujan bulanan di DKI Jakarta memiliki variabilitas tinggi dan distribusi yang menjulur ke kanan, sehingga prediksinya memerlukan pendekatan probabilistik. Penelitian ini bertujuan menerapkan model Bayesian Model Averaging (BMA) campuran tiga tingkat hierarki yaitu global, musim, dan bulan yang menggabungkan distribusi Gamma dan Weibull, menentukan pembobotannya secara berbasis data, serta membandingkan kinerjanya dengan model tunggal di Stasiun Kemayoran dan Stasiun Maritim Tanjung Priok. Parameter diestimasi dengan Maximum Likelihood Estimation Newton–Raphson sebagai nilai awal, dilanjutkan inferensi Bayesian melalui Markov Chain Monte Carlo pada ketiga tingkat. Bobot antardistribusi Gamma dan Weibull dan bobot antartingkat ditentukan dari data melalui aproksimasi BIC. Model divalidasi dengan skema expanding window pada 12 bulan (Januari–Desember 2025) dan dievaluasi menggunakan Continuous Ranked Probability Score (CRPS). Hasil menunjukkan seluruh rantai MCMC konvergen (Rˆ < 1,01) dan model terkalibrasi baik dengan 100% observasi berada dalam interval kredibel 90% pada kedua stasiun. Pembobotan bersifat adaptif tiap bulan, dengan tingkat bulan memperoleh bobot rata-rata terbesar (0,398 di Kemayoran dan 0,415 di Tanjung Priok). Berdasarkan mean CRPS, model BMA memperoleh kinerja terbaik di kedua stasiun, yaitu 73,21 di Kemayoran dan 47,79 di Tanjung Priok, dengan selisih kurang dari 1% terhadap model tunggal. Dengan demikian, BMA campuran hierarki menghasilkan prediksi probabilistik yang robust terhadap ketidakpastian pemilihan model dan distribusi. ***** Monthly rainfall in DKI Jakarta exhibits high variability and a right-skewed distribution, so its prediction requires a probabilistic approach. This study aims to apply a three-level hierarchical Bayesian Model Averaging (BMA) mixture that is global, seasonal, and monthly which combining the Gamma and Weibull distributions, to determine its weights in a data-driven manner, and to compare its performance against single models at the Kemayoran Station and the Tanjung Priok Maritime Station. Parameters were estimated using Newton–Raphson Maximum Likelihood Estimation as starting values, followed by Bayesian inference via Markov Chain Monte Carlo at all three levels. The within-level (Gamma andWeibull) and between-level weights were determined from the data through a BIC approximation. The model was validated using an expanding-window scheme over 12 months (January–December 2025) and evaluated using the Continuous Ranked Probability Score (CRPS). The results show that all MCMC chains converged (Rˆ < 1.01) and the model was well calibrated, with 100% of observations falling within the 90% credible interval at both stations. The weighting was adaptive across months, with the monthly level receiving the largest average weight (0.398 at Kemayoran and 0.415 at Tanjung Priok). Based on the mean CRPS, the BMA model achieved the best performance at both stations which is 73.21 at Kemayoran and 47.79 at Tanjung Priok, with less than a 1% margin over the single models. Thus, the hierarchical BMA mixture yields probabilistic predictions that are robust to model and distribution selection uncertainty

Item Type:	Thesis (Sarjana)
Additional Information:	1). Drs. Sudarwanto, M.Si., DEA; 2). Devi Eka Wardani MEganingtyas, S.Pd., M.Si.
Subjects:	Sains > Matematika
Divisions:	FMIPA > S1 Matematika
Depositing User:	Elvin Fernando .
Date Deposited:	21 Aug 2026 08:25
Last Modified:	21 Aug 2026 08:25
URI:	http://repository.unj.ac.id/id/eprint/72789

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