From a statistical perspective, functional mapping estimates parameters that determine the shape of a genotype-specific growth curve and/or the covariance structure, thus strikingly increasing its statistical power for QTL detection. Functional mapping was originally constructed within the maximum likelihood (ML) context, incorporated by a finite mixture model and implemented with the EM algorithm [11; 12]. Although ML-based approaches have many favorable statistical properties for parameter estimation, they may often face some significant drawbacks when applied to functional mapping. First, functional mapping usually uses nonlinear mathematical equations to model the mean and covariance structures, it is extremely difficult or eventually impossible to derive log-likelihood equations for nonlinear parameters in the maximization step. Second, functional mapping concerns genetic analyses of longitudinal data whose intrinsic high-dimensional complexity makes computation increasingly prohibitive, especially when permutation tests are used to determine critical thresholds. Third, but not specific to functional mapping, ML-based approaches do not automatically provide confidence interval estimates of the estimators, and thus affect the inference of parameter estimation. Many of the problems described above for ML can be overcome by using a Bayesian method. In ML, the unknown parameters are treated as unknown variables (unobservables) and the likelihood function is maximized in these variables. In the Bayesian paradigm, each unobservable parameter is given a prior distribution, and we then infer the posterior distribution of each unobservable conditional on the data (the observables). The summary statistics of the posterior distribution, e.g., the mean, the mode or the median, can be regarded as Bayesian estimates of unobservables [13]. The interval estimate can be obtained simply by examining the posterior distribution. The mean of this marginal posterior distribution is a candidate Bayesian estimator of an unknown parameter. Although this marginal distribution rarely has an explicit form, and numerical integration is often prohibited because of high dimensionality of parameters, a Markov chain Monte Carlo (MCMC) algorithm can be used to simulate the sample from the joint posterior distribution. The potential of the Bayesian approach implemented with the Gibbs sampler or Metropolis-Hastings algorithm for QTL mapping has been explored for various genetic designs [14; 15; 16; 17; 18]. [PERSON] and [PERSON] [19] incorporated a Bayesian approach to map QTLs involved in a dynamic trait based on nonparametric Legendre polynomials, although they did not take a full advantage of functional mapping in quantifying biologically meaningful hypothesis tests about the genetic control of development and modeling the structure of the covariance matrix. For such biological processes as growth curve, HIV dynamics and pharmacodynamics, in which explicit mathematical functions exist to specify their dynamic changes, functional mapping based on parametric modeling has proven to be powerful for asking and addressing the biological questions at the interplay between genetic actions and developmental patterns. In longitudinal data analysis, parametric covariance modeling has several advantages compared to conventional multivariate approaches ignoring the covariance structure. The most significant advantage is that parametric modeling generally results in more efficient estimation of the covariance matrix (and therefore the mean structure). Also, it can deal more effectively with data when the number of measurement times is relatively large. Lastly, it can handle the data more effectively in the cases that the measurement times are not common across subjects. For those reasons, the development of explicit parametric models for the variance-covariance structure has been an important topic over the last two decades [20; 21].