Keeping up with the GMRFs

Turns out the family of GMRFs is quite a motley one. Researchers have specified these models in varied fashion across the body of literature. Here are some prime examples:

  1. Intrinsic (Improper)
  2. Linear filters specification as in the perturb-and-MAP paper.
  3. Via the covariance matrix
  4. Generalized CAR
  5. Besag's classical zero-mean CAR
  6. AR/SAR.
The CAR vs SAR dilemma was pretty informational as Katt Williams put it. The bottom line seems to be that SAR models are sorta more well suited to ML estimation (but not so much for MCMC fitting). The
hierarchical conditional representation of CAR helps it trump here. 
*Must read more*