Here is a short list of some of the courses I have taken, with links and summaries that may be useful. These materials are free to download. If you feel they are useful, you can donate any amount of money to danioyuan (at) hotmail (dot) com to encourage the author to spend more effort on making and sharing more information of this kind.
Probability Theory and Mathematical Statistics II (summary)
Instructed by Professor S.C. Samuel Kou
Introduction to statistical inference. Frequency, Bayesian, and decision-theoretic approaches. Likelihood, sufficiency, and exponential families. Testing hypotheses and estimation. Maximum likelihood estimation, likelihood ratio tests, Bayes Factor, models for frequency data, large and moderate sample approximations, including the delta method.
Introduction to Stochastic Processes (summary)
Instructed by Professor Jun S. Liu
An introductory course in stochastic processes. Topics include Markov chains, branching processes, Poisson processes, birth and death processes, renewal theory, queuing theory, Brownian motion, and Martingales.
Probability Theory and Mathematical Statistics (summary)
Instructed by Professor Carl N. Morris
Random variables, their distributions and densities. Families of distributions. Expectation. Independence, product spaces, and joint distributions. Types of convergence. Limit theorems. Conditional probability and expectation, multivariate Normal distribution, conjugate, marginal, and conditional distributions. Inequalities, approximations, and stochastic simulation. Sampling distributions, likelihood function, sufficiency, and information.
Design of Experiments (summary)
Instructed by Professor Rima Izem
Statistical designs for the estimation of the effects of treatments in randomized experiments. Topics include brief review of some basic structural inference procedures, analysis of variance, randomized block and Latin square designs, balanced incomplete block designs, factorial designs, nested factorial designs, confounding in blocks, and fractional replications.
Spatial Statistics (summary)
Instructed by Professor Rima Izem
Introduction of three types of spatial data: point pattern, geospatial, and lattice. For each type of data, presentation and application of statistical and computational methods for description, modeling, and analysis.
Lectured by Dr. Gopi Goswami
This course is aimed at implementing statistical algorithms (mainly Monte Carlo algorithms, e.g. Metropolis-Hastings, Sequential Monte Carlo, E-M etc.) in R with a backend support of C or C++. In other words, we want to make use of C or C++ to make R implementations faster.