BAYESIAN LOGISTIC REGRESSION USING GAUSSIAN NAÏVE BAYES

J. F. Ojo, R.O.Olanrewaju, & S.A.Folorunsho

Department of Statistics,

University of Ibadan, Ibadan, Nigeria.

Email: jfunminiyiojo@yahoo.co.uk, rasakiolawale@gmail.com, serifatf005@gmail.com,

ABSTRACT

This study describes the approach of Gaussian Naïve Bayes (GNB) as a prior distribution classifier in a two-class (dichotomous) classification of the posterior probability of the dependent variable in a Bayesian logistic regression.   This approach establishes the procedure for parameter estimation of Bayesian logistic regression when we could not ascertained whether the prior distribution is informative or non-informative. The Newton-Raphson iterative procedure was used in estimating the vector parameters because there was no closed-form solution due to non-linearity of the logistic function. This study was applied to four set of panaceas drugs on diarrhea treatment for babies less than a year old (Nigeria Demographic Health Survey (NDHS, 2013)). It was noted that the standard errors of parameters estimated via Bayesian logistic regression using the GNB were lower than that of standard errors of parameters estimated via the Classical Logistic Regression (CLR) using the Maximum Likelihood Estimation (MLE), which makes Bayesian logistic regression via GNB better than CLR.

Keywords: Gaussian Naïve Bayes, Bayesian Logistic Regression, Maximum Likelihood Estimation, Posterior Distribution, Prior Distribution.