Chapter 7: Bayesian Estimation

Learning Objectives

• Formulate estimation problems in the Bayesian framework: prior, likelihood, posterior
• Derive and compute the MAP and MMSE estimators for standard models
• Prove that the MMSE estimator is the conditional mean via the orthogonality principle
• Construct the LMMSE estimator from second-order statistics and compute its error covariance
• Recognize when MMSE, LMMSE, and MAP coincide (jointly Gaussian case)
• Apply Bayesian estimation to pilot-based channel estimation (LS vs. MMSE)