Posterior propriety in nonparametric mixed effects model

It is well known that spline smoothing estimator relates to the Bayesian estimate under partially informative normal prior. In this paper, we derive the conditions for the propriety of the posterior in the nonparametric mixed effects model under this class of partially informative normal prior for fixed effect with inverse gamma priors on the variance components and hierarchical priors for covariance matrix of random effect, then we explore the Gibbs sampling procedure.