estimateMVbeta(y, x, Sigma, maxIter = 200, epsilon = 1e-06, verbose = FALSE, nknots = 10, nOut = 2000, nIn = 4000, iterInit = 3, br = NULL)$$y|c \sim N(\mu,c\Sigma)$$ $$c \sim \mbox{InvGamma}(m/2,m\nu/2)$$ where $v$ is function of the covariate x: $v(x)$ and $N$ denotes a multivariate normal distribution, $Sigma$ is a covariance matrix and $InvGamma(a,b)$ is the inverse-gamma distribution with density function $$f(x)=(\beta)^{\alpha} \exp\{-\beta/x\} x^{-\alpha-1}/\Gamma(\alpha)$$
A cubic spline is used to parameterize the smooth function $v(x)$ $$\nu(x) = \exp\{ H(x)^T \beta \}$$ where $H:R->R^(2p-1)$ is a set B-spline basis functions for a given set of p interior spline-knots, see chapter 5 of Hastie (2001). In this application $mu$ equals zero, and m is the degrees of freedom.
Hastie, T., Tibshirani, R., and Friedman, J. (2001). The Elements of Statistical Learning, volume 1. Springer, first edition.
Kristiansson, E., Sj$o$gren, A., Rudemo, M., Nerman, O. (2005). Weighted Analysis of Paired Microarray Experiments. Statistical Applications in Genetics and Molecular Biology 4(1)
$A$strand, M. et al. (2007a). Improved covariance matrix estimators for weighted analysis of microarray data. Journal of Computational Biology, Accepted.
$A$strand, M. et al. (2007b). Empirical Bayes models for multiple-probe type arrays at the probe level. Bioinformatics, Submitted 1 October 2007.