STAT 242b / STAT 542b Theory of Statistics
Study of the principles of statistical analysis. Topics include maximum likelihood, sampling distributions, estimation, confidence intervals, tests of significance, regression, analysis of variance, and the method of least squares. Some statistical computing.
STAT 682a High-Dimensional Function Estimation
Modern developments of high-dimensional function estimation, building from classical one-dimensional ingredients. Theory and methods for approximation, estimation, and computation. The blessing and the curse of high-dimensionality. Piece-wise polynomial, sinusoidal, and sigmoidal (artificial neural network) models. Product and ridge-basis models. Selection criteria. Deterministic and stochastic optimization strategies, including gradient methods, greedy algorithms, annealing and the associated theory of evolution of the parameters of the function estimates. Students will be responsible for a literature-based theory project/presentation and a computational project/presentation.