### Current MSCS Graduate Courses ( Fall 2018, Spring 2019 )

### Fall 2018

#### STAT 501

Probability Theory I (Ouyang)- PREREQUISITES:
- MATH 534 or consent of instructor.
- DESCRIPTION:
- Abstract measure theory, probability measures, Kolmogorov extension theorem, sums of independent random variables, the strong and weak laws of large numbers, the central limit theorem, characteristic functions, law of iterated logarithm, infinitely divisible laws. http://www.math.uic.edu/~jyang06/stat501/stat501.html

#### STAT 521

Linear Statistical Inference (Wang)- PREREQUISITES:
- STAT 411 and STAT 481.
- DESCRIPTION:
- Estimation and testing in linear models, generalized inverses of matrices, n-dimensional normal distribution, quadratic forms, estimable parameter, normal equations, analysis of variance, likelihood ratio tests.

#### STAT 591

Advanced Topics in Statistics, Probability, and Operations Research: Wu (TBD)- PREREQUISITES:
- TBD
- DESCRIPTION:
- TBD

### Spring 2019

#### STAT 502

Probability Theory II (Ouyang)- PREREQUISITES:
- STAT 501.
- DESCRIPTION:
- Radon-Nikodym theorem, conditional expectations, martingales, stationary processes, ergodic theorem, stationary Gaussian processes, Markov chains, introduction to stochastic processes, Brownian motions.

#### STAT 511

Advanced Statistical Theory I (Wu)- PREREQUISITES:
- STAT 411.
- DESCRIPTION:
- Statistical models, criteria of optimum estimation, large sample theory, optimum tests and confidence intervals, best unbiased tests in exponential families, invariance principle, likelihood ratio tests.

#### STAT 522

Multivariate Statistical Analysis (Yang, J.)- PREREQUISITES:
- STAT 521.
- DESCRIPTION:
- Multivariate normal distribution, estimation of mean vector and covariance matrix, T-square statistic, discriminant analysis, general linear hypothesis, principal components, canonical correlations, factor analysis

#### STAT 531

Sampling Theory I (Hedayat)- PREREQUISITES:
- Stat 411.
- DESCRIPTION:
- Foundations of survey design and inference for finite populations; the Horvitz-Thompson estimator; simple random, cluster, systematic survey designs; auxiliary size measures in design and inference.

#### STAT 535

Optimal Design Theory I (Yang, M.)- PREREQUISITES:
- Stat 521.
- DESCRIPTION:
- Gauss-Markov theorem, optimality criteria, optimal designs for 1-way, 2-way elimination of heterogeneity models, repeated measurements, treatment-control; Equivalence theorem, approximate designs for polynomial-regression.

#### STAT 591

Adv Top in Stat, Probability, and Operations Research: Stochastic Calculus in Math Finance (Ouyang)- PREREQUISITES:
- Stat 501 and 502, or consent of instructor.
- DESCRIPTION:
- The theory: Brownian motion, Continues time martingales, Markov properties of Brownian motion, Construction of Brownian motion, Stochastic integrals, Itˆo’s formula, Applications of Itˆo’s formula, The Girsanov theorem. Applications to math ﬁnance: Black-Scholes formula, local volatility models and the fundamental theorem of ﬁnance.

#### STAT 591

Advanced Topics in Statistics, Probability, and Operations Research (Hedayat)- PREREQUISITES:
- TBD
- DESCRIPTION:
- TBD