Maximum Likelihood Estimation: Theory and Examples

This lecture introduces the concept of maximum likelihood estimation, focusing on the proof of the Rao-Blackwell Theorem and its application in deriving unbiased estimators. The instructor explains the importance of sufficient statistics and demonstrates how to calculate maximum likelihood estimators through examples such as Bernoulli, Exponential, and Gaussian trials. The lecture concludes with an example of Poisson observations, emphasizing the process of determining the maximum likelihood estimator. Throughout the lecture, the instructor emphasizes the significance of selecting estimators that contain the most relevant information from the sample data.