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Bayesian Post-Model-Selection Estimation
IEEE Signal Processing Letters ( IF 3.9 ) Pub Date : 2021-01-05 , DOI: 10.1109/lsp.2020.3048830
Nadav Harel , Tirza Routtenberg

Estimation after model selection refers to the problem where the exact observation model is unknown and is assumed to belong to a set of candidate models. Thus, a data-based model-selection stage is performed prior to the parameter estimation stage, which affects the performance of the subsequent estimation. In this letter, we investigate post-model-selection Bayesian parameter estimation of a random vector with an unknown deterministic support set, where this support set represents the model. First, we present different estimators, including the oracle minimum mean-squared-error (MMSE), the coherent MMSE, the selected MMSE, and the full model MMSE. Then, we develop the selective Bayesian Cram $\acute{\text{e}}$ r-Rao bound (BCRB) and selective tighter BCRB, which are lower bounds on the mean-squared-error (MSE) for any coherent estimator.

中文翻译:

贝叶斯模型选择后估计

模型选择后的估计是指确切的观测模型未知且假定属于一组候选模型的问题。因此,在参数估计阶段之前执行基于数据的模型选择阶段,这会影响后续估计的性能。在这封信中,我们调查了具有未知确定性支持集的随机向量的模型选择后贝叶斯参数估计,其中该支持集代表模型。首先,我们提出了不同的估计量,包括预兆最小均方误差(MMSE),相干MMSE,所选MMSE和完整模型MMSE。然后,我们开发选择性贝叶斯补习班 $ \ acute {\ text {e}} $ r-Rao界(BCRB)和选择性更严格的BCRB,这是任何相干估计的均方误差(MSE)的下界。
更新日期:2021-01-29
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