### 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.

Original language | Malay |
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Pages (from-to) | 227-235 |

Number of pages | 9 |

Journal | Sains Malaysiana |

Volume | 48 |

Issue number | 1 |

DOIs | |

Publication status | Published - 1 Jan 2019 |

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### ASJC Scopus subject areas

- General

### Cite this

*Sains Malaysiana*,

*48*(1), 227-235. https://doi.org/10.17576/jsm-2019-4801-26

**Pentaabiran Bayesian untuk Model Regresi Linear Prior Normal-Pencong-Alfa.** / Alhamide, A. A.; Ibrahim, Kamarulzaman; Alodat, M. T.; Wan Zin @ Wan Ibrahim, Wan Zawiah.

Research output: Contribution to journal › Article

*Sains Malaysiana*, vol. 48, no. 1, pp. 227-235. https://doi.org/10.17576/jsm-2019-4801-26

}

TY - JOUR

T1 - Pentaabiran Bayesian untuk Model Regresi Linear Prior Normal-Pencong-Alfa

AU - Alhamide, A. A.

AU - Ibrahim, Kamarulzaman

AU - Alodat, M. T.

AU - Wan Zin @ Wan Ibrahim, Wan Zawiah

PY - 2019/1/1

Y1 - 2019/1/1

N2 - 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.

AB - 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.

KW - ABSTRAK

KW - Alpha skew normal distribution

KW - Bayesian linear regression model

KW - Simulation

UR - http://www.scopus.com/inward/record.url?scp=85062302453&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85062302453&partnerID=8YFLogxK

U2 - 10.17576/jsm-2019-4801-26

DO - 10.17576/jsm-2019-4801-26

M3 - Article

VL - 48

SP - 227

EP - 235

JO - Sains Malaysiana

JF - Sains Malaysiana

SN - 0126-6039

IS - 1

ER -