On the Markov Chain Monte Carlo Convergence Diagnostic of Bayesian Finite Mixture Model for Income Distribution

The assessment and comparison of income inequality and poverty can be supported by estimating the probability distribution of income. Income distributions which are typically heavy-tailed and positively skewed have been estimated both parametric and nonparametric approach. In parametric approach, finite mixtures distributions have been usefully implemented in the modelling of income distributions which has the multimodal characteristic. The Markov Chain Monte Carlo (MCMC) approach is one of the estimation methods which has a good performance in estimating the parameter of Bayesian finite mixture model. The convergence of the MCMC sampler to the posterior distribution is typically assessed using standard diagnostics methods, i.e., Gelman-Rubin method, Geweke method, Raftery-Lewis method and Heidelberger-Welch method. Those methods can give different results to conclude MCMC convergence condition. In this paper, a real sample income data from the Indonesian Family Life Survey (IFLS) 2015 and BidikMisi 2015 are employed to demonstrate the performance of diagnostics tools that assess convergence of the MCMC algorithm in estimating the parameter of Bayesian finite mixture models.