COMPARATIVE ANALYSIS OF BAYESIAN ESTIMATION TECHNIQUES FOR GAMMA DISTRIBUTIONS

This paper explores the estimation of the common scale parameter for two Gamma populations using three Bayesian methods: Approximate Bayesian Computation (ABC), Hamiltonian Monte Carlo (HMC), and Metropolis-Hastings (MH). Unlike traditional methods like Maximum Likelihood Estimation (MLE), which can be sensitive to model misspecification, these Bayesian methods are more flexible in handling parameter uncertainty and complex data. ABC bypasses explicit likelihood calculations, HMC improves sampling efficiency through gradient information, and MH offers simplicity and adaptability. A simulation study compares these methods based on bias, mean squared error (MSE), and computational efficiency. Additionally, we apply these methods to real glucose level data from male and female individuals with diabetes, highlighting their strengths and limitations. The results offer practical recommendations for real-world applications involving Gamma distributions, contributing to the advancement of Bayesian estimation techniques in complex parameter estimation problems.