Sains Malaysiana 48(1)(2019): 227–235

http://dx.doi.org/10.17576/jsm-2019-4801-26

 

Bayesian Inference for Linear Regression under Alpha-Skew-Normal Prior

(Pentaabiran Bayesian untuk Model Regresi Linear Prior Normal-Pencong-Alfa)

 

ALHAMIDE, A.A.¹, KAMARULZAMAN IBRAHIM², ALODAT, M.T.¹ & WAN ZAWIAH WAN ZIN^2*

 

¹Department of Mathematics, Statistics and Physics, Qatar University, Qatar

 

²Pusat Pengajian Sains Matematik, Fakulti Sains dan Teknologi, Universiti Kebangsaan Malaysia, 43600 UKM Bangi, Selangor Darul Ehsan, Malaysia

 

Diserahkan: 5 September 2017/Diterima: 3 Ogos 2018

 

ABSTRACT

A study on Bayesian inference for the linear regression model is carried out in the case when the prior distribution for the regression parameters is assumed to follow the alpha-skew-normal distribution. The posterior distribution and its associated full conditional distributions are derived. Then, the Bayesian point estimates and credible intervals for the regression parameters are determined based on a simulation study using the Markov chain Monte Carlo method. The parameter estimates and intervals obtained are compared with their counterparts when the prior distributions are assumed either normal or non-informative. In addition, the findings are applied to Scottish hills races data. It appears that when the data are skewed, the alpha-skew-normal prior contributes to a more precise estimate of the regression parameters as opposed to the other two priors.

 

Keywords: Alpha skew normal distribution; Bayesian linear regression model; simulation

 

ABSTRAK

Suatu kajian tentang pentaabiran Bayesian untuk model regresi dijalankan untuk kes taburan prior bagi parameter regresi yang diandaikan mengikuti taburan normal-pencong-alfa. Taburan posterior dan taburan bersyarat penuh yang berkaitan diterbitkan. Seterusnya, anggaran titik dan selang boleh percaya Bayesian ditentukan berdasarkan satu kajian simulasi menggunakan kaedah rantai Markov Monte Carlo. Anggaran titik dan selang yang diperoleh dibandingkan dengan keputusan apabila taburan diandaikan normal dan tak bermaklumat. Di samping itu, penemuan ini digunakan untuk data perlumbaan bukit Scottish. Kajian ini mendapati bahawa dalam kes data pencong, penganggaran parameter adalah lebih tepat apabila prior normal-pencong-alfa diandaikan berbanding prior normal dan tak bermaklumat.

 

Kata kunci: Model regresi linear Bayesian; simulasi; taburan normal-pencong-alfa

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*Pengarang untuk surat-menyurat; email: w_zawiah@ukm.edu.my