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In this paper, we develop a generalized Bayesian inference framework for acollection of signal-plus-noise matrix models arising in high-dimensionalstatistics and many applications. The framework is built upon an asymptoticallyunbiased estimating equation with the assistance of the leading eigenvectors ofthe data matrix. The solution to the estimating equation coincides with themaximizer of an appropriate statistical criterion function. The generalizedposterior distribution is constructed by replacing the usual log-likelihoodfunction in the Bayes formula with the criterion function. The proposedframework does not require the complete specification of the samplingdistribution and is convenient for uncertainty quantification via a MarkovChain Monte Carlo sampler, circumventing the inconvenience of resampling thedata matrix. Under mild regularity conditions, we establish the large sampleproperties of the estimating equation estimator and the generalized posteriordistributions. In particular, the generalized posterior credible sets have thecorrect frequentist nominal coverage probability provided that the so-calledgeneralized information equality holds. The validity and usefulness of theproposed framework are demonstrated through the analysis of synthetic datasetsand the real-world ENZYMES network datasets.

Eigenvector-Assisted Statistical Inference for Signal-Plus-Noise Matrix Models