Mean-Square-Error Inference

This lecture covers the fundamental concept of mean-square-error inference, focusing on the estimation of unaccessible parameters or random variables from related observations. It introduces the mean-square-error (MSE) criterion and discusses inference problems using the MSE criterion. The lecture explores different design criteria for inference purposes, such as mean-absolute error (MAE) and maximum a-posteriori (MAP) criteria. It delves into the inference without observations, estimation problems, and the concept of conditional mean estimator. The lecture also discusses the optimal choice for minimizing mean-square-error and the derivation of optimal estimators using completion-of-squares. It concludes with examples illustrating the application of optimal estimators in practical scenarios.