Pendekatan Bayesian Pada Model Regresi Polinomial

Sutanto, Hery Tri (2007) Pendekatan Bayesian Pada Model Regresi Polinomial. Masters thesis, Institut Teknologi Sepuluh November.

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Abstract

Jika y variabel respon x variabel bebas maka model regresi polinomial j (Mⱼ) adalah : Y = β₀ + β₁x + β₂x² + ... + βⱼxʲ + ε, 0 < j ≤ d. Dalam pemilihan model polinomial terbaik dari data machine setting yang digunakan and banyaknya energy consumption yang dihabiskan, dengan menggunakan empat metode, pertama Intrinsic Bayes Factor, kedua Fractional Bayes Factor, ketiga Bayesian Information Criterion dan keempat Markov Chain Monte Carlo. Pada metode Intrinsic Bayes Factor sampel yang tersedia dipotong kecil-kecil dengan ukuran sampel sesuai banyaknya parameter setiap polinomial ditambah satu, sehingga diperoleh beberapa sampel training yang mungkin. Sampel yang tersedia dibagi menjadi dua, sampel training dan sampel tersisa. Distribusi posterior pada sampel training digunakan sebagai distribusi prior pada pemodelan sampel tersisa sehingga nilai Bayes Factor dapat ditentukan. Sedangkan metode Fractional Bayes Factor dengan memilih suatu bilangan fractional yang merupakan pembagian ukuran sampel training dengan ukuran sampel yang tersedia dan menghitung fungsi likelihood dari kedua model polinomial sehingga nilai Bayes Factor dapat diperoleh. Kemudian metode Bayesian Information Criterion menentukan log likelihood dan banyaknya parameter untuk setiap model polinomial sehingga nilai Bayes Factor ditentukan. Kelima model polinomial dapat diestimasi dengan Markov Chain Monte Carlo dengan menentukan densitas prior dari masing-masing parameter dalam setiap model polinomial dalam program Minitab, selanjutnya kelima model polinomial diadu dalam struktur perkalian distribusi sehingga nilai Bayes Factor diperoleh. Untuk keempat metode di atas terlihat bahwa model polinomial order 5 paling mewakili data ukuran mesin yang digunakan, dengan banyaknya energy consumption yang dihabiskan dibandingkan model polinomial order di bawahnya pada metode Intrinsic Bayes Factor; model polinomial order 4 paling mewakili data ini dibandingkan model polinomial order 0, 1, 2, 3 dan 5 pada metode Fractional Bayes Factor; model polinomial order 4 paling mewakili data dibandingkan model polinomial order lainnya pada Bayesian Information Criterion, dan model polinomial orde 4 merupakan model terbaik pada Markov Chain Monte Carlo.
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If Y is dependent variable and x independent variable, then the order polynomial regression model j (Mⱼ) is : Y = β₀ + β₁x + β₂x² + ... + βⱼxʲ + ε, 0 < j ≤ d. The selection model for the best polynomial models of data between relation machine setting that used and number of energy consumption that used with fourth methods, the first is Intrinsic Bayes Factor, the second Fractional Bayes Factor, the third Bayesian Information Criterion, and the fourth Markov Chain Monte Carlo. By Intrinsic Bayes Factor models, samples divided by number of every parameter of polynomials and added one, then get the possible any training sample. The samples divided into two, training samples and remaining samples. Posterior distribution at training samples used as prior distribution at modeling remaining samples then Bayes Factor result can be obtained. Fractional Bayes Factor method using with choosing a number of fractional as denominator of training sample size with measure of sample and count for likelihood function from both of polynomials then Bayes Factor can be obtained. Then Bayesian Information Criterion (BIC) method used to obtain log likelihood and number of parameters for every polynomial models then Bayes Factor can be obtained. All of polynomial models can be estimated with using Markov Chain Monte Carlo by calculated prior density at each parameter in every polynomial model in Minitab program. The polynomial models compare in distribution's multiplying structure then Bayes Factor result can be obtained. For the four of the method, looks the fifth order of polynomial model most represent of data machine's measure that used. The number of energy consumption that used comparing by the lower of order polynomial at Intrinsic Bayes Factor method. The fourth order of polynomial model most represent data comparing by 0, 1, 2, 3, and 5 order of polynomial model at Fractional Bayes Factor method; the fourth polynomial model most represent the data comparing by another order of polynomial model at Bayesian Information Criterion, and the fourth order of polynomial model as a most fit model at Markov Chain Monte Carlo.

Item Type:	Thesis (Masters)
Additional Information:	RTSt 519.542 Sut p
Uncontrolled Keywords:	Bayes Factor, Bayesian Jnformation Criterion, Fractional Bayes Factor,Markov Chain Monte Carlo, model polinomial.
Subjects:	Q Science > QA Mathematics > QA279.5 Bayesian statistical decision theory.
Divisions:	Faculty of Mathematics and Science > Statistics > 49101-(S2) Master Thesis
Depositing User:	magang .
Date Deposited:	30 Sep 2026 08:33
Last Modified:	30 Sep 2026 08:33
URI:	http://repository.its.ac.id/id/eprint/145105

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