Beyond likelihood-Based Inference: A Detailed Bayesian Paradigm for Heavy-Tailed Reliability data
Keywords:
Bayesian approach, Convergence diagnostics, Markov chain Monte Carlo (MCMC), Predictive performance, Survival analysisAbstract
This study explores the Bayesian analysis of Modified Logistic Lomax distribution. Markov Chain Monte Carlo (MCMC) is used for the parameter estimation using a real dataset. Convergence Diagnostics, Predictive performances and Inferential Survival Characteristics are analysed. The P-P and Q-Q plots, as well as the Posterior Survival plot and Hazard rate plots demonstrate excellent fitting of the distribution under Bayesian parameter estimations. The model demonstrated excellent convergence (R-hat < 1.01) and superior predictive accuracy (WAIC = 917.4). The 95% credible intervals for Mean Survival Time (128.52-137.20) practically supports the utility of this framework. This study contributes to the Bayesian literature on probability and inferential statistics as well as to the future researcher for analysing real data sets using Bayesian approaches. All the computational analysis of the study is performed using R-language programming.
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