  Multivariate Bayesian error-in-variable (EIV) linear regression is considered
to account for additional additive Gaussian error in the features and response.
A 3-variable deterministic scan Gibbs samplers is constructed for multivariate
EIV regression models using classical and Berkson errors with independent
normal and inverse-Wishart priors. These Gibbs samplers are proven to always be
geometrically ergodic which ensures a central limit theorem for many time
averages from the Markov chains. We demonstrate the strengths and limitations
of the Gibbs sampler with simulated data for large data problems, robustness to
misspecification and also analyze a real-data example in astrophysics.
