.png){kind=icon}
Return
Estimation Performance for the Bayesian Hierarchical Linear Model
.png){kind=icon}
OA
AI
DOI：10.1109/LSP.2016.2528579.png)
.png){kind=icon}
.png){kind=icon}
Share.png){kind=icon}
Save
Abstract
En 中文
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.
Keywords:
Bayesian Cramer-Rao bound
hierarchical linear model
performance analysis
AI Summary
Key information extracted from the uploaded paper, including a brief overview, abstract, background, key highlights, visual analysis, and future outlook.
Journal
IF:
9.6
Papers:
1.1W
Citations:
1.7W
Organization
Cited Papers
ShareSaveShareSaveRECENT RADIATION OF ENDEMIC CARIBBEAN DROSOPHILA OF THE DUNNI SUBGROUP INFERRED FROM MULTILOCUS DNA SEQUENCE VARIATION.png)
EvolutionOAAI
EvolutionIF0
OAAIShareSave
View more