Parameter Estimation of Bayesian Multiple Regression Model with Informative Inverse Gamma Prior Distribution: Application to Malaria Symptom Dataset

Abstract

Objectives: The study aims to develop a Bayesian multiple regression model with informative inverse gamma prior and t the model to malaria symptom dataset. Place and Duration of Study: The study was carried out in Masinde Muliro University of Science and Technology (MMUST). The study used 300 malaria related symptom dataset obtained from Health service records of different patients (students) between the time period of 1st January, 2015 to 20th December, 2015. Methodology: Multiple linear regression model with Bayesian parameter estimation is used. The Normal prior distribution for θ parameter and inverse gamma prior distribution for the σ2 parameter is derived. Gibbs sampler and Metropolis Hasting algorithm is used with Markov Chain Monte Carlo (MCMC) method to produce an iteration of about 102,491 with Burn-in of 2500 and thinning of 10 that resulting to eective sample size of 90000. Results: The results shows that all the estimated posterior predictive p-values are between 0.05 and 0.95 indicating an adequate t for the individual observation of the data in the model. The results also reveals that the data values and the average distance between the data values and the mean tend to be close to each other and the estimated coeffcient of θ′s approximately 95%draws fall within each of the corresponding highest posterior density intervals. Conclusion: Though the Least Squares method is sucient for estimating the coeffcients of the regression parameters, the Bayesian estimates recorded comparatively very small standard errors making the Bayesian method more robust in analysing symptom dataset.