Hierarchical tree model for a generic Gaussian field f on the sky. Itis decomposed into an amplitude field A_f containing the correlation structure and an a priori white Gaussian field ξ_f connecting this correlation information to the actual spatial representation. A_f on its own again depends on hyper-priors σ_f l_f and another white field ζ_f. This tree wraps up Appendix B and is the core building block of our correlation structure inference.