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arXiv · 2503.13046

On a conjecture of Roverato regarding G-Wishart normalising constants

Ching Wong·Giusi Moffa·Jack Kuipers
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Abstract

The evaluation of G-Wishart normalising constants is a core component for Bayesian analyses for Gaussian graphical models, but remains a computationally intensive task in general. Based on empirical evidence, Roverato [Scandinavian Journal of Statistics, 29:391--411 (2002)] observed and conjectured that such constants can be simplified and rewritten in terms of constants with an identity scale matrix. In this note, we disprove this conjecture for general graphs by showing that the conjecture instead implies an independently-derived approximation for certain ratios of normalising constants. We further show that the conjecture is actually a saddle-point approximation, allowing us to derive the next-order correction which enables more accurate evaluation.

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Ching Wong, Giusi Moffa, Jack Kuipers. 2025-03-17. On a conjecture of Roverato regarding G-Wishart normalising constants. https://arxiv.org/abs/2503.13046

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