On the Stability of Bayesian Bifurcated Autoregressive Process via Student-t Random Noise: Application and Simulation
Rasaki Olawale Olanrewaju, Sodiq Adejare Olanrewaju, Wasiu Adesoji Adepoju · Universal Journal of Applied Mathematics · 2024
In this article, we proposed and thoroughly described Bayesian bifurcated autoregressive process with student-t pairwise auto-correlated random noises for degenerated, lineage, or segmentation characterization process that usually lead to bifurcated autoregressive process. An informative prior of the Beta distributional form, that is, , for bifurcated autoregressive coefficients that ranges from [0,1], that is, , was proposed in conjunction with an Inverted-Gamma ( ) distribution for the student-t distributed likelihood. The derived posterior distribution for the emerged priors and likelihood yielded a conjugated multivariate student-t like-distribution. Markov Chain Monte Carlo (MCMC) based approach in an embedded Metropolis-within-Gibbs algorithm was used to estimate the Bayesian bifurcated autoregressive coefficients, and it was ascertained that the derived posterior distribution takes a quadratic form of the multivariate student-t density. The posterior solutions of the Bayesian bifurcated autoregressive process were applied to eight imbalanced classes of a strain bacterial infection called Escherichia coli sequence and simulation studies, such that the obtained results were compared with the classical bifurcated autoregressive and ordinary autoregressive results. The merit of the Bayesian bifurcated autoregressive process over the classical bifurcated autoregressive process and autoregressive process was that the estimated bifurcated autoregressive coefficients via posterior solutions were stable across the application of the Escherichia coli sequence and simulation studies with a reduced bias-corrected method of Boot and LBC.