292 / FIELDS OF INSTRUCTION


 Prerequisite: STA 640. Notions of convergence of sequences of independent
 random variables: continuity theorem, law of large numbers, central limit theorem.
 STA 642-PROBABILITY THEORY 3. 4 credits
 Prerequisite: STA 641. Dependence, Martingale Convergence Theorem, the
 law of large numbers and central limit theorems for dependent random variables.
 STA 650-NONPARAMETRIC STATISTICS. 4 credits
 Prerequisite: STA 612. Hypothesis testing, power and asymptotic relative
 efficiency of tests. Rank tests, tests of goodness of fit, robust estimators, and
 order statistics.
 STA 652-SEQUENTIAL ANALYSIS. 4 credits
 Prerequisite: STA 612. Sequential likelihood ratio tests of two competing simple
 hypotheses. Operating characteristics, average sample number, and optimal prop-
 erties.
 STA 660-STOCHASTIC PROCESSES 1. 3 credits
 Prerequisite: STA 610. Discrete time and state models. Gambler's Ruin. Per-
 sistent and transient states: long run and stationary distribution mean absorption
 times, mean first passage times.
 STA 661-STOCHASTIC PROCESSES 2. 3 credits
 Prerequisite: STA 660. Continuous time, discrete state models. Poisson, general-
 ized Poisson, and filtered Poisson processes. Polya process. Birth and death models.
 Application to the theory of queues and inventories.
 STA 662-STOCHASTIC PROCESSES 3. 3 credits
 Prerequisite: STA 661. Wiener-Levy process; Ornstein Uhlenbeck process. In-
 tegrated processes. White noise and thermal noise. Applications of stochastic
 processes in the physical sciences.
 STA 670-MULTIVARIATE ANALYSIS 1. 4 credits
 Prerequisite: STA 619. Multivariate tests of hypotheses. Construction of multi-
 variate confidence regions, multivariate analysis of variance, discriminant analysis
 and tests of independence.
 STA 671-MULTIVARIATE ANALYSIS 2. 4 credits
 Prerequisite: STA 670. Continuation of STA 670.
 STA 680-TIME SERIES 1. 4 credits
 Prerequisite: STA 641 or STA 661. Statistical theory of stationary time
 series; estimation and tests of hypotheses concerning the spectral density.
 STA 681-TIME SERIES 2. 4 credits
 Prerequisite: STA 680. Statistical analysis of parametric models; distribution of
spectral estimates.
STA 682-TIME SERIES 3. 4 credits
 Prerequisite: STA 681. Problems in linear estimation. Applications and recent
developments discussed in journal articles.
STA 683-ADVANCED PROBABILITY THEORY 1. 4 credits
 Prerequisite: MS 643. Probability at the level of Loeve's "Probability Theory."
Probability, independence, and dependence.
STA 684-ADVANCED PROBABILITY THEORY 2. 4 credits
 Prerequisite: STA 683. Continuation of STA 683.
STA 690-SPECIAL TOPICS IN STATISTICS. 4 credits
 Prerequisite: Permission of the graduate adviser. Assigned reading of lecture
series in advanced statistics. May be repeated with change of content up to a maxi-
mum of 18 credits.