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STAT 494: Special Topics in Statistics, Probability and Operations Research
3.00 - 4.00 Credits
University of Illinois at Chicago
Course content announced prior to each semester in which it is given. Topics drawn from areas such as distribution theory; Bayesian inference; discrete optimization; applied probability models; resampling techniques; biostatistics; environmental sampling. 3 undergraduate hours. 4 graduate hours. May be repeated. Students may register in more than one section per term. Prerequisite(s): Approval of the department.
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STAT 494 - Special Topics in Statistics, Probability and Operations Research
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STAT 496: Independent Study
1.00 - 4.00 Credits
University of Illinois at Chicago
Reading course supervised by a faculty member. May be repeated. Students may register in more than one section per term. Prerequisite(s): Approval of the instructor and approval of the department.
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STAT 496 - Independent Study
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STAT 501: Probability Theory I
4.00 Credits
University of Illinois at Chicago
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. Prerequisite(s): MATH 534 or consent of the instructor.
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STAT 501 - Probability Theory I
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STAT 502: Probability Theory II
4.00 Credits
University of Illinois at Chicago
Radon-Nikodym theorem, conditional expectations, martingales, stationary processes, ergodic theorem, stationary Gaussian processes, Markov chains, introduction to stochastic processes, Brownian motions. Prerequisite(s): STAT 501.
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STAT 502 - Probability Theory II
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STAT 511: Advanced Statistical Theory I
4.00 Credits
University of Illinois at Chicago
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. Prerequisite(s): STAT 411.
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STAT 511 - Advanced Statistical Theory I
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STAT 512: Advanced Statistical Theory II
4.00 Credits
University of Illinois at Chicago
Basic concepts in decision theory, prior and posterior distributions, Bayesian decision theory, hierarchical models, robustness, minimax analysis, invariance principle, sequential analysis, completeness. Prerequisite(s): STAT 511.
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STAT 512 - Advanced Statistical Theory II
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STAT 521: Linear Statistical Inference
4.00 Credits
University of Illinois at Chicago
Estimation and testing in linear models, generalized inverses of matrices, n-dimensional normal distribution, quadratic forms, likelihood ratio tests, best invariant tests, analysis of variance. Prerequisite(s): STAT 411.
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STAT 521 - Linear Statistical Inference
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STAT 522: Multivariate Statistical Analysis
4.00 Credits
University of Illinois at Chicago
Multivariate normal distribution, estimation of mean vector and covariance matrix, T-square statistic, discriminant analysis, general linear hypothesis, principal components, canonical correlations, factor analysis. Prerequisite(s): STAT 521.
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STAT 522 - Multivariate Statistical Analysis
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STAT 531: Sampling Theory I
4.00 Credits
University of Illinois at Chicago
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. Prerequisite(s): STAT 411.
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STAT 531 - Sampling Theory I
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STAT 532: Sampling Theory II
4.00 Credits
University of Illinois at Chicago
Uses of auxiliary size measures in survey sampling; cluster sampling; systematic sampling; stratified sampling; superpopulation methods; randomized response methods; resampling; nonresponse; small area estimations. Prerequisite(s): STAT 531.
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STAT 532 - Sampling Theory II
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