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Quasi-Bayesian estimation of large Gaussian graphical models

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  • Atchadé, Yves F.

Abstract

This paper deals with the Bayesian estimation of large precision matrices in Gaussian graphical models. We develop a quasi-Bayesian implementation of the neighborhood selection method of Meinshausen and Bühlmann (2016). The method produces a product-form quasi-posterior distribution that can be efficiently explored by parallel computing. Under some restrictions on the true precision matrix, we show that the quasi-posterior distribution contracts in the spectral norm at the rate of O{s⋆ln(p)∕n}, where p is the number of nodes in the graph, n the sample size, and s⋆ is the maximum degree of the undirected graph defined by the true precision matrix. We develop a Markov Chain Monte Carlo algorithm for approximate computations, following an approach from Atchadé (2019). We illustrate the methodology using real and simulated data examples.

Suggested Citation

  • Atchadé, Yves F., 2019. "Quasi-Bayesian estimation of large Gaussian graphical models," Journal of Multivariate Analysis, Elsevier, vol. 173(C), pages 656-671.
    • Handle: RePEc:eee:jmvana:v:173:y:2019:i:c:p:656-671
    DOI: 10.1016/j.jmva.2019.03.005
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