Efficient　estimation　of　the　regression　coefficients　in　longitudinal　data　analysis　requires　a　correct　specification　of　the　covariance　structure.　If　misspecification　occurs,　it　may　lead　to　inefficient　or　biased　estimators　of　parameters　in　the　mean.　One　of　the　most　commonly　used　methods　for　handling　the　covariance　matrix　is　based　on　simultaneous　modeling　of　the　Cholesky　decomposition.　Therefore,　in　this　paper,　we　reparameterize　covariance　structures　in　longitudinal　data　analysis　through　the　modified　Cholesky　decomposition　of　itself.　Based　on　this　modified　Cholesky　decomposition,　the　within-subject　covariance　matrix　is　decomposed　into　a　unit　lower　triangular　matrix　involving　moving　average　coefficients　and　a　diagonal　matrix　involving　innovation　variances,　which　are　modeled　as　linear　functions　of　covariates.　Then,　we　propose　a　fully　Bayesian　inference　for　joint　mean　and　covariance　models　based　on　this　decomposition.　A　computational　efficient　Markov　chain　Monte　Carlo　method　which　combines　the　Gibbs　sampler　and　Metropolis-Hastings　algorithm　is　implemented　to　simultaneously　obtain　the　Bayesian　estimates　of　unknown　parameters,　as　well　as　their　standard　deviation　estimates.　Finally,　several　simulation　studies　and　a　real　example　are　presented　to　illustrate　the　proposed　methodology.