Rejoinder on: Some recent work on multivariate Gaussian Markov random fields

I thank the discussants, Miguel A. Martinez-Beneito, Fedel Greco, Carlo Trivisano, Stephan R Sain, and Reinhard Furrer, for their insightful and stimulating commentary. The rejoinder is organized in five sections: (1) the M-based models, (2) posterior sensitivity to prior choices for \({\varvec{C}}\) and \({\varvec{\varSigma }}\), (3) stationary and non-stationary (M)GMRFs, (4) various approaches to model formulation and related applications, and (5) statistical computation.