MATH8654

This course aims to introduce the basic methodology, theory, and algorithms for probabilistic modeling. Specifically, the course is divided into three parts. The first part (and majority) of the course will cover fundamentals of statistical inference, including likelihood-based estimation methods, asymptotic theory, Bayesian statistics, nonparametric models (e.g. nonparametric regression, Gaussian process), minmax theory. The second part will focus on statistical sampling algorithms, with emphasis on Markov Chain Monte Carlo methods. The last part (if time permits) will cover inference for sequential data, with emphasis on filtering and data assimilation.