Vitenskapelig artikkel   2018

Uhler, Caroline; Lenkoski, Alex; Richards, Donald

Publication details

Journal:

Annals of Statistics, vol. 46, p. 90–118, 2018

Publisher:

Institute of Mathematical Statistics

Issue:

1

International Standard Numbers:

Printed: 0090-5364
Electronic: 2168-8966

Links:

DOI: doi.org/10.1214/17-AOS1543

Gaussian graphical models have received considerable attention during the past four decades from the statistical and machine learning communities. In Bayesian treatments of this model, the G-Wishart distribution serves as the conjugate prior for inverse covariance matrices satisfying graphical constraints. While it is straightforward to posit the unnormalized densities, the normalizing constants of these distributions have been known only for graphs that are chordal, or decomposable. Up until now, it was unknown whether the normalizing constant for a general graph could be represented explicitly, and a considerable body of computational literature emerged that attempted to avoid this apparent intractability. We close this question by providing an explicit representation of the G-Wishart normalizing constant for general graphs.