Document Type : Revised File ( Second edition)


Department of Statistics, Tarbiat Modares University, Tehran, Iran.


‎Beta regression models are useful for modeling continuous rates (proportions) affected by independent variables‎. ‎Sometimes in the Bayesian inference of these models‎, ‎the posterior distributions would not be constructed in closed form‎. ‎Markov chain Monte Carlo algorithms for solving related integrals due to no small number of parameters may be time-consuming even faced with the problem of divergence‎. ‎Using approximate Bayesian inference could be a solution for obtaining these posterior distributions‎. ‎In this paper‎, ‎the Bayesian Beta regression models are presented‎. ‎The Integrated Nested Laplace Approximation will be offered for getting the posterior distributions in the analysis of these models‎. ‎Moreover‎, ‎these models' application is illustrated on a real data set‎.