Modern information processing systems deal with massive amounts of data in the presence of large statistical uncertainty. The performance and behaviors of such systems often exhibit phase transitions (e.g., threshold SNR, cutoff rates, etc.), due to the interactions of a large number of random variables with complex correlation structures. Methods developed in statistical physics have been tremendously successful in understanding the macroscopic properties of many-body interactive systems. They have also been gradually recognized as an indispensable tool in the study of
This course introduces students to probability theory and statistics, and their applications in engineering. Topics include: random variables, distributions and densities, conditional expectations, limit theorems, Bernoulli and Poisson processes, Markov chains, Bayesian statistical inferences and parameter estimations. The goal of this course is to prepare students with adequate knowledge of probability theory and statistical methods, which will be useful in the study of several advanced undergraduate/graduate courses and in formulating practical engineering problems.
This graduate-level course introduces students to detection and estimation theory, with applications to communications, control, imaging, and image processing. Topics include hypothesis testing; linear and non-linear estimation; maximum likelihood and Bayes approaches; stochastic processes and systems; signal detection and estimation in noise; decision-theory concepts; optimum-receiver principles and Markov chain Monte Carlo techniques.