Sains Malaysiana 44(10)(2015): 1417–1422

Outlier Detection using Generalized Linear Model in Malaysian Breast Cancer Data

(Pengesanan Nilai Tersisih menggunakan Model Linear Teritlak dalam Data Kanser Payudara Malaysia)

M. NAWAMA¹, A.I.N. IBRAHIM¹*, I.B. MOHAMED¹, M.S. YAHYA¹ & N.A.M. TAIB²

¹Institute of Mathematical Sciences, University of Malaya, 59100 Kuala Lumpur, Malaysia

²Department of Surgery, University of Malaya Medical Centre, 59100 Kuala Lumpur, Malaysia

Received:  22 March 2013/Accepted:  15 June 2015

ABSTRACT

We consider the problem of outlier detection in bivariate exponential data fitted using the generalized linear model via Bayesian approach. We follow closely the work outlined by Unnikrishnan (2010) and present every step of the detection procedure in details. Due to the complexity of the resulting joint posterior distribution, we obtain the information on the posterior distribution from samples generated by Markov Chain Monte Carlo sampling, in particular, using either the Gibbs sampler or the Metropolis-Hastings algorithm. We use local breast cancer patients’ data to illustrate the implementation of the method.

Keywords: Bayesian; Gibbs sampler; Metropolis-Hastings algorithm; Outlier

ABSTRAK

Kami mempertimbangkan masalah pengesanan nilai tersisih dalam data bivariat eksponen dengan menggunakan model linear teritlak melalui pendekatan Bayesian. Kami mengikuti secara rapat kajian yang digariskan oleh Unnikrishnan (2010) dan membentangkan setiap langkah prosedur pengesanan secara terperinci. Disebabkan kerumitan taburan posterior tercantum yang terhasil, kami mendapatkan maklumat mengenai taburan posterior tersebut daripada sampel yang dijana oleh pensampelan Markov Chain Monte Carlo, khususnya, menggunakan sama ada kaedah pensampelan Gibbs atau algoritma Metropolis-Hastings yang umum. Kami menggunakan data tempatan iaitu data pesakit kanser payudara untuk menggambarkan pelaksanaan kaedah tersebut.

Kata kunci: Algoritma Metropolis-Hastings; Bayesian; kaedah pensampelan Gibbs; nilai tersisih

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