TY - JOUR
T1 - Bayesian Post-Model-Selection Estimation
AU - Harel, Nadav
AU - Routtenberg, Tirza
N1 - Funding Information:
Manuscript received September 22, 2020; revised November 22, 2020; accepted December 15, 2020. Date of publication January 5, 2021; date of current version January 28, 2021. This research was supported in part by the Israel Science Foundation (ISF) under Grant 1173/16. The work of Nadav Harel was supported by the Kreitman School of Advanced Graduate Studies. The associate editor coordinating the review of this manuscript and approving it for publication was Dr. John Ball. (Corresponding author: Tirza Routtenberg.) The authors are with the School of Electrical and Computer Engineering, Ben-Gurion University of the Negev, Beersheba 84105, Israel (e-mail: nadavhar@post.bgu.ac.il; tirzar@bgu.ac.il).
Publisher Copyright:
© 1994-2012 IEEE.
PY - 2021/1/1
Y1 - 2021/1/1
N2 - 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.
AB - 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.
KW - Bayesian parameter estimation
KW - coherence estimation
KW - estimation after model selection
KW - selective Bayesian Cramer-Rao bound
KW - sparse recovery
UR - http://www.scopus.com/inward/record.url?scp=85099249093&partnerID=8YFLogxK
U2 - 10.1109/LSP.2020.3048830
DO - 10.1109/LSP.2020.3048830
M3 - Article
AN - SCOPUS:85099249093
SN - 1070-9908
VL - 28
SP - 175
EP - 179
JO - IEEE Signal Processing Letters
JF - IEEE Signal Processing Letters
M1 - 9314021
ER -