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Estimation Performance for the Bayesian Hierarchical Linear Model
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DOI：10.1109/LSP.2016.2528579.png)
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摘要
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Bayesian hierarchical modelling is a well-established branch of Bayesian inference. In this letter, we derive and study the estimation performance for the Bayesian hierarchical linear model (BHLM). Specifically, we consider a linear model with hierarchical priors for the involved amplitude and noise vectors. We provide closed-form expressions of the Bayesian Cramer-Rao bound (BCRB) for the following settings: (i) an arbitrary prior and hyperprior and (ii) a Gaussian-Y prior for the amplitudes, while the prior of noise is a Gaussian-X in both cases. Gaussian-X means that the conditional prior given the hyperparameter is Gaussian and X is the hyperprior. For the hierarchical distribution associated with spherical invariant random variables, the BCRB has a compact closed-form expression and enjoys several interesting properties that are discussed. Finally, we provide a theoretical analysis of the statistical efficiency of the linear minimum mean square error (MMSE) estimator in the low-and high-noise variance regimes when the hyperparameters are stochastically dominant.
Keyword:
Bayesian Cramer-Rao bound
hierarchical linear model
performance analysis
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IF:
9.6
论文数:
1.1W
被引数:
1.7W
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