# A Loss-Based Prior for Gaussian Graphical Models

arXiv: https://arxiv.org/abs/1812.05531 · HTML: https://mlsanity.com/paper/1812.05531/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 13 Dec 2018.

## Built on by (most cited first, 1 of 1)

- [Bayesian model selection of vine copulas: a loss-based perspective](https://mlsanity.com/paper/2606.21512/) (2026)

## Abstract (arXiv)

Gaussian graphical models play an important role in various areas such as genetics, finance, statistical physics and others. They are a powerful modelling tool which allows one to describe the relationships among the variables of interest. From the Bayesian perspective, there are two sources of randomness: one is related to the multivariate distribution and the quantities that may parametrise the model, the other has to do with the underlying graph, G, equivalent to describing the conditional independence structure of the model under consideration. In this paper, we propose a prior on G based on two loss components. One considers the loss in information one would incur in selecting the wrong graph, while the second penalises for large number of edges, favouring sparsity. We illustrate the prior on simulated data and on real datasets, and compare the results with other priors on G used in the literature. Moreover, we present a default choice of the prior as well as discuss how it can be calibrated so as to reflect available prior information.