Exact formulas for the normalizing constants of Wishart distributions for graphical models
Name
1406.4901.pdf
Description
Submitted version
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572.79 KB
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Unknown
Checksum (MD5)
6bc3dffbe99c88d0e176915c1b84e707
Author(s)
Uhler, Caroline
Lenkoski, Alex
Richards, Donald
Date Issued
2018
Journal
The Annals of Statistics
Publisher
Institute of Mathematical Statistics
Version
Original manuscript
Abstract
© Institute of Mathematical Statistics, 2018. 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.
MIT Department
Massachusetts Institute of Technology. Department of Electrical Engineering and Computer Science
Massachusetts Institute of Technology. Institute for Data, Systems, and Society
Terms of Use
Creative Commons Attribution-Noncommercial-Share Alike
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DOI of Published Version
https://doi.org/10.1214/17-AOS1543
