Maximum Likelihood Estimation: Multivariate Statistics

This lecture covers preliminary results on maximum likelihood estimation for multivariate normal distributions, including the log-likelihood function, MLEs for mean and covariance, and hypothesis testing strategies. Examples illustrate the challenges of testing multiple hypotheses and the difference between univariate and multivariate testing. The union intersection test is introduced as an approach to test multiple hypotheses simultaneously. The instructor, Erwan Koch from EPFL's Institute of Mathematics, provides theoretical foundations and practical examples to understand the complexities of multivariate hypothesis testing.