Maximum Likelihood: Estimation and Inference

This lecture covers the concept of maximum likelihood (ML) estimation, a powerful tool in statistical analysis for inferring unknown parameters by fitting probability density functions to data measurements. The lecture introduces the ML approach, discussing its properties and applications in modern statistical analysis. It also explores the formulation of ML in solving inference problems, such as estimating parameters for Gaussian and Beta distributions. Additionally, the lecture delves into the Cramer-Rao lower bound, which provides a limit on the variance of unbiased estimators, and discusses the properties of unbiasedness, efficiency, and consistency in the context of ML estimators.