Likelihood Ratio Test: Neyman-Pearson Lemma

This lecture delves into the concept of likelihood ratio tests, focusing on the Neyman-Pearson Lemma. The instructor explains how to construct the most powerful test for detecting a specific distribution when the true data come from that distribution. By comparing likelihood ratios and setting thresholds, the lecture demonstrates how to make decisions based on statistical analysis. The discussion extends to scenarios with multiple parameters and complex hypotheses, emphasizing the importance of maximizing likelihood ratios to determine the best test. Through examples involving normal distributions and t-statistics, the lecture illustrates practical applications of the Neyman-Pearson approach in hypothesis testing.