Short Course Description
Overview of the parameter estimation problem. Estimation in parametric families. Minimum variance unbiased estimation. Fisher information and the Cramer-Rao lower bound. Linear models and least-squares estimation. The complete sufficient statistics approach. Exponential families. Maximum likelihood estimation and its asymptotic properties. Bayesian estimation: MMSE estimation, Maximum A-Posteriori (MAP) estimation, conjugate priors. Regularization: connection to Bayesian theory, sparse models. Hypothesis testing (detection theory): Bayesian setting, Neyman-Pearson setting, sample complexity, composite hypothesis testing and GLRT. Minimax estimation: Bayesian lower bounds, Le Cam's method. Algorithms: sequential estimation, alternating-minimization, coordinate descent.
Full syllabus is to be published
