TY - GEN
T1 - Multivariate Priors and the Linearity of Optimal Bayesian Estimators under Gaussian Noise
AU - Barnes, Leighton P.
AU - Dytso, Alex
AU - Liu, Jingbo
AU - Poor, H. Vincent
N1 - This work was supported in part by a grant from the C3.ai Digital Transformation Institute.
PY - 2024
Y1 - 2024
N2 - Consider the task of estimating a random vector X from noisy observations Y=X+Z, where Z is a standard normal vector, under the Lp fidelity criterion. This work establishes that, for 1≤ p ≤ 2, the optimal Bayesian estimator is linear and positive definite if and only if the prior distribution on X is a (non-degenerate) multivariate Gaussian. Furthermore, for p > 2, it is demonstrated that there are infinitely many priors that can induce such an estimator.
AB - Consider the task of estimating a random vector X from noisy observations Y=X+Z, where Z is a standard normal vector, under the Lp fidelity criterion. This work establishes that, for 1≤ p ≤ 2, the optimal Bayesian estimator is linear and positive definite if and only if the prior distribution on X is a (non-degenerate) multivariate Gaussian. Furthermore, for p > 2, it is demonstrated that there are infinitely many priors that can induce such an estimator.
UR - http://www.scopus.com/inward/record.url?scp=85202847813&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=85202847813&partnerID=8YFLogxK
U2 - 10.1109/ISIT57864.2024.10619358
DO - 10.1109/ISIT57864.2024.10619358
M3 - Conference contribution
AN - SCOPUS:85202847813
T3 - IEEE International Symposium on Information Theory - Proceedings
SP - 987
EP - 992
BT - 2024 IEEE International Symposium on Information Theory, ISIT 2024 - Proceedings
PB - Institute of Electrical and Electronics Engineers Inc.
T2 - 2024 IEEE International Symposium on Information Theory, ISIT 2024
Y2 - 7 July 2024 through 12 July 2024
ER -