Sains Malaysiana 48(4)(2019): 893–899

http://dx.doi.org/10.17576/jsm-2019-4804-22

 

Outlier Detection in 2 × 2 Crossover Design using Bayesian Framework

(Pengesanan Titik Terpencil dalam 2 × 2 Reka Bentuk Pindah Silang Menggunakan Rangka Kerja Bayesian)

 

F.P. LIM^1,2, I.B. MOHAMED¹*, A.I.N. IBRAHIM¹, S.L. GOH³ & N.A. MOHAMED @ A. RAHMAN¹

 

¹Institute of Mathematical Sciences, University of Malaya, 50603 Kuala Lumpur, Federal Territory, Malaysia

 

²Faculty of Sciences, Universiti Putra Malaysia, 43400 UPM Serdang, Selangor Darul Ehsan, Malaysia

 

³Sport Medicine Clinic, University of Malaya Medical Centre, 50603 Kuala Lumpur, Federal Territory, Malaysia

 

Received: 23 April 2016/Accepted: 20 January 2019

 

ABSTRACT

We consider the problem of outlier detection method in 2×2 crossover design via Bayesian framework. We study the problem of outlier detection in bivariate data fitted using generalized linear model in Bayesian framework used by Nawama. We adapt their work into a 2×2 crossover design. In Bayesian framework, we assume that the random subject effect and the errors to be generated from normal distributions. However, the outlying subjects come from normal distribution with different variance. Due to the complexity of the resulting joint posterior distribution, we obtain the information on the posterior distribution from samples by using Markov Chain Monte Carlo sampling. We use two real data sets to illustrate the implementation of the method.

 

Keywords: Bayesian; crossover design; Markov Chain Monte Carlo; outlier

 

ABSTRAK

Kami mengambil kira masalah kaedah pengesanan nilai terpencil dalam kajian pindah silang 2×2 melalui rangka kerja Bayesian. Kami mengkaji masalah pengesanan titik tersisih bagi data bivariat yang disuaikan dengan model linear teritlak dalam rangka kerja Bayesian yang digunakan oleh Nawama. Kami menyesuaikan kerja-kerja tersebut ke dalam 2×2 kajian pindah silang. Dalam rangka kerja Bayesian, kami menganggap bahawa kesan subjek rawak dan ralat akan dijana daripada taburan normal. Walau bagaimanapun, nilai terpencil pula tertabur normal dengan varians yang berbeza. Disebabkan taburan posterior tercantum yang kompleks, kami mendapatkan maklumat mengenai taburan posterior daripada sampel yang dijana melalui pensampelan Markov Chain Monte Carlo (MCMC). Kami menggunakan dua set data sebenar untuk menggambarkan pelaksanaan kaedah tersebut.

 

Kata kunci: Bayesian; Markov Chain Monte Carlo; reka bentuk pindah silang; titik terpencil

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*Corresponding author; email: imohamed@um.edu.my