22S:102 INTRODUCTION TO STATISTICAL METHODS (3 s.h.)
Same as 07P:143.
Questions regarding this course should be directed to the Department of Psychological and Quantitative Foundations, 335-5577.
22S:105 STATISTICAL METHODS AND COMPUTING (3 s.h.)
Meets with 22S:030. Emphasis is on learning statistical methods and concepts through hands-on experience with real data using the statistical software package SAS. During scheduled Early Registration, enrollment is restricted to majors in statistics, biological sciences, and mechanical and industrial engineering. Further registrations are granted by consent of the instructor.
Prerequisite: 22M:002.
Offered spring semesters.
Syllabus: Spring 2008 | Spring 2007
22S:120 PROBABILITY AND STATISTICS (4 s.h.)
This is a first course in probability and mathematical statistics that can follow two semesters of calculus. If students intend to take a least two semesters' work in this area, they should take 22S:130 and 22S:131 instead. Material covered includes probability models, discrete and continuous random variables, expectations, estimation of parameters, hypothesis testing, and regression. Graduate students in the Department of Statistics and Actuarial Science cannot use this course on their Plan of Study.
Prerequisite: 22M:026 or 22M:032.
Offered fall and spring semesters, and summer sessions.
Syllabus: Spring 2008 | Fall 2007 | Summer 2007 | Spring 2007
22S:130 INTRODUCTION TO MATHEMATICAL STATISTICS I (3 s.h.)
This course is an introductory sequence on probability and mathematical statistics that is appropriate for undergraduate majors in statistics or actuarial science. This is an expanded version of 22S:120. The first semester of the sequence concentrates on probability, random variables, discrete and continuous distributions, conditional probability, and expectation. Graduate students in the Department of Statistics and Actuarial Science cannot use this course on their Plan of Study.
Prerequisite: 22M:026 or 22M:032.
Offered fall semesters.
Syllabus: Fall 2007
22S:131 INTRODUCTION TO MATHEMATICAL STATISTICS II (3 s.h.)
This is a continuation of 22S:130. The primary focus is on statistical inference. Topics include properties of estimators, confidence intervals, hypothesis testing, and regression.
Prerequisite: 22S:130.
Offered spring semesters.
Syllabus: Spring 2008 | Spring 2007
22S:133 QUALITY CONTROL (3 s.h.)
Prerequisite: 22S:039.
Same as 056:162.
22S:138 BAYESIAN STATISTICS (3 s.h.)
Bayesian statistical analysis, with focus on applications; Bayesian and frequentist methods compared; Bayesian model specification, choice of priors, computational methods; hands-on Bayesian data analysis using appropriate software; interpretation and presentation of analysis results.
Prerequisite: 22S:120 and 22S:152 or equivalent.
Same as 07P:148.
Offered fall semesters.
Syllabus: Fall 2007
22S:140 DESIGN AND ANALYSIS OF BIOMEDICAL STUDIES (3 s.h.)
Prerequisite: 171:161.
Same as 171:162.
22S:148 INTERMEDIATE STATISTICAL METHODS (3 s.h.)
Prerequisite: 22S:102 or equivalent.
Same as 07P:243.
22S:150 REGRESSION, TIME SERIES, AND FORECASTING (3 s.h.)
Regression analysis, forecasting, time series methods; use of statistical computing packages.
Prerequisite: 22S:131 or 22S:154.
Offered fall semesters.
Syllabus: Fall 2007
22S:152 APPLIED LINEAR REGRESSION (3 s.h.)
Regression analysis with focus on applications; model formulation, checking, selection; interpretation and presentation of analysis results; simple and multiple linear regression; logistic regression; ANOVA; hands-on data analysis with computer software.
Prerequisite: 22S:030 or 22S:039 or 22S:043 or 22S:102 or equivalent.
Same as 056:176.
Offered fall semesters.
Syllabus: Fall 2007
22S:153 MATHEMATICAL STATISTICS I (3 s.h.)
This is a course in mathematical statistics which is taught at a higher level than 22S:130 and 22S:131. Undergraduate students often complete 22S:120 or 22S:130 prior to taking the course; the latter stresses conditional distributions, functions of random variables, and basic concepts of convergence. Completion of undergraduate calculus (including linear algebra) is a prerequisite. Usually requirements include two midterms, homework, a few quizzes, and a final exam.
Prerequisites: 22M:027 and 22M:028 or equivalents.
Offered fall and spring semesters.
Syllabus: Spring 2008 | Fall 2007 (Sec 001), Fall 2007 (Sec 002), Fall 2007 (Sec 003) | Spring 2007
22S:154 MATHEMATICAL STATISTICS II (3 s.h.)
This course is a continuation of 22S:153. It is intended for upper-level undergraduate students in the mathematical sciences as well as for graduate students in all disciplines. The goal is to give students a solid foundation in the theory and methods of statistical inference. Topics include convergence in distribution and convergence in probability, as well as point estimation, confidence intervals, and testing of statistical hypotheses. Both frequentist and Bayesian paradigms are discussed and examined. Grades are determined on the basis of midterms, weekly homework and/or quizzes, and a final exam.
Prerequisite: 22S:153 or equivalent.
Offered fall and spring semesters.
Syllabus: Spring 2008 (sec 001), Spring 2008 (sec 002) | Fall 2007 | Spring 2007 (sec 001), Spring 2007 (sec 002)
22S:156 APPLIED TIME SERIES ANALYSIS (3 s.h.)
This course covers the analysis and modeling of time series data. Time series are observations that become available sequentially in time. Examples include monthly unemployment rates, quarterly data on economic indicators, and hourly data on air pollutants. The course gives an introduction to the theory and applications of time series analysis. Emphasis is on the time-domain approach to time series analysis, but a brief introduction to the frequency domain approach also is given. Autocorrelation and spectral density functions, stationarity, and autoregressive integrated moving average models for nonseasonal and seasonal time series are discussed. Additional topics are volatility models, multivariate models and nonlinear models. Illustration is provided on how to construct such models from data, and students discuss the specification on these models, the estimation of their parameters, diagnostic checks to assess their validity, and the predictions that are implied by these models. Statistical computer packages are used throughout. Requirements include two midterms, a term project involving analysis of real time series data, and several homework and computer assignments.
Prerequisites: 22S:131; and 22S:152 or 22S:164.
Offered spring semesters.
Syllabus: Spring 2008 | Spring 2007
22S:157 CORRELATION AND REGRESSION (4 s.h.)
Prerequisite: 22S:148 or equivalent.
Same as 07P:244.
22S:158 EXPERIMENTAL DESIGN AND ANALYSIS (3 s.h.)
Single- and multifactor experiments; analysis of variance; multiple comparisons; contrasts; diagnostics, fixed, random, and mixed effects models; designs with blocking and/or nesting; two-level factorials and fractions thereof; use of statistical computing packages.
Prerequisites: 22S:030 and 22S:152.
Offered spring semesters of odd years, typically.
Syllabus: Spring 2008 | Spring 2007
22S:159 DESIGN OF EXPERIMENTS (4 s.h.)
Prerequisite: 22S:148.
Same as 07P:246.
22S:160 INTRODUCTORY LONGITUDINAL DATA ANALYSIS (3 s.h.)
Same as 171:174.
22S:161 APPLIED MULTIVARIATE ANALYSIS (3 s.h.)
MANOVA, discriminant analysis, factor analysis, principal components, canonical analysis, nonmetric scaling, cluster analysis, categorical data analysis, use of multivariate statistical computer packages.
Prerequisites: 22S:152 and 22S:158, or equivalents; and facility with matrix algebra.
Same as 07P:245.
Offered fall semesters of odd years.
Syllabus:
22S:162 APPLIED GENERALIZED REGRESSION (3 s.h.)
Review of least squares and normal linear models. Applications of semi-parametric models, generalized linear models, nonlinear normal errors models, correlated response models. Use of statistical packages, especially SAS.
Prerequisites: introductory statistics and applied linear models.
Offered spring semesters of even years, typically.
Syllabus: Fall 2007
22S:163 NONPARAMETRIC STATISTICAL METHODS (3 s.h.)
One- and two-sample location tests and estimation methods, measures of association and analysis of variance; emphasis on relationship with classical parametric procedures.
Prerequisite: 22S:120 or 22S:148 or consent of instructor.
Same as 07P:247.
Syllabus:
22S:164 APPLIED STATISTICS I (4 s.h.)
This course is the first of a two-course sequence on applied statistics. It is a required course for the M.S. in Statistics and is generally taken by first-year statistics graduate students. However, others with adequate statistical background also may take it. The course is included on the M.S. comprehensive exam for statistics. The objectives are to give students a solid foundation in some of the most important, broadly used statistical methods, and to give students experience in applying those methods to data using statistical computing packages and interpreting results. Topics include descriptive statistics, confidence intervals in one-sample and two-sample problems, t and F tests, chi-square tests, and multiple regression analysis (including model fitting, diagnostics, selection, and testing).
Prerequisites: 22S:120 or equivalent, and facility with matrix algebra.
Offered fall semesters.
Syllabus: Fall 2007
22S:165 APPLIED STATISTICS II (3 s.h.)
This course primarily concerns the design of experiments. Topics include practical issues (formulation of research goals, selection of experimental units, randomization, and blocking), modeling, sample-size determination, analysis of variance, follow-up comparisons, graphical displays, and handling certain messy-data situations. The course emphasizes understanding the complexities of designs; besides covering several classical designs (factorial, crossover, split-plot, etc.), students will learn to model and analyze experiments for an unfamiliar design. Participants will analyze data from a variety of disciplines, and also conduct and analyze their own experiments, either real or by computer simulation. Much (but not all) of the software emphasis is on SAS. Grades are determined based on homework, exams, and one or more projects that involve writing a report that presents an experiment, its analysis, and its scientific conclusions.
Prerequisite: 22S:164 or equivalent.
Offered spring semesters.
Syllabus: Spring 2008 | Spring 2007
22S:166 COMPUTING IN STATISTICS (3 s.h.)
Linux operating system; R and SAS (statistical computing environments); LaTeX (mathematical document preparation language); database management; graphical techniques; WinBUGS (software for fitting Bayesian models); simulation methods (Monte Carlo studies, bootstrap, MCMC); statistical computing algorithms (Newton's method, EM algorithm).
Prerequisites: 22S:153, 22S:154, 22S:164 and 22S:165, or equivalents.
Offered fall semesters.
Syllabus: Fall 2007
22S:167 ENVIRONMENTAL AND SPATIAL STATISTICS (3 s.h.)
The goal of this course is to learn how to statistically analyze and interpret environmental and spatial data. The course covers methods for sampling environmental populations, geostatistics and kriging, and spatial lattice and point pattern analysis. Applications to environmental monitoring data and spatial disease mapping are featured.
Prerequisites: 22S:152 and 22S:154, or equivalents.
Offered spring semesters of odd years.
Syllabus: Spring 2007
22S:168 INTERMEDIATE EXPERIMENTAL DESIGN (3 s.h.)
Continuation of 22S:165, which is prerequisite; factorial and fractional factorial designs; response surface methods; canonical analysis; product/process robustness experiments; advanced topics in design.
Prerequisite: 22S:165.
Offered fall semesters of even years.
Syllabus:
22S:171 TOPICS IN ACTUARIAL SCIENCE (3 s.h.)
This course is intended for students who are studying for the professional examination on Construction and Evaluation of Actuarial Models given by the Casualty Actuarial Society and the Society of Actuaries. It covers severity, frequency and aggregate models of insurance losses, and statistical methods to estimate parameters of such models from sample data. It is a required course for all graduate students in actuarial science.
Corequisite: 22S:180.
Syllabus: Spring 2008 | Spring 2007
22S:172 TOPICS IN STATISTICS (3 s.h.)
Prerequisite: 22S:154 or consent of instructor.
Syllabus: Spring 2008 (sec 001), Spring 2008 (sec 002)
22S:173 STATISTICAL CONSULTING (3 s.h.)
This course covers data analysis topics in conjunction with observation and interaction with clients doing research in areas of application. Data analysis topics include interacting with clients, writing and presenting reports, graphical methods, a broad overview of statistical methods (parametric, nonparametric, robust, paired and independent samples, small and large sample), sample-size computations for different situations, and how large sample sizes need to be in order to use asymptotic results. Other topics are discussed as they arise in connection with client projects. Instructor has the option of using S-U grades for Graduate College, School of Management, and graduate students in the College of Public Health. Grading is based on homework, quizzes, and written reports and oral presentations of consulting problems.
Prerequisites: 22S:152 and 22S:158; or 22S:164 and 22S:165.
Offered spring semesters.
Syllabus: Spring 2008 | Spring 2007
22S:174 QUANTITATIVE METHODS FOR ACTUARIES (3 s.h.)
Algorithms, finite differences; interpolation; linear and quadratic programming; individual risk models; life tables.
Prerequisites: multivariate calculus and linear algebra.
Corequisites: 22S:153 or 22S:193.
Offered fall semesters.
Syllabus: Fall 2007
22S:175 ACTUARIAL MODELS (3 s.h.)
Poisson processes; compound Poisson processes; Markov chains; Brownian motion; simulation; financial applications. This is a required course for all students in actuarial science.
This course meets occasionally on Saturday mornings for exams.
Prerequisite: grade of C or higher in 22S:174.
Offered spring semesters.
Syllabus: Spring 2008 | Spring 2007
22S:176 CREDIBILITY AND LOSS DISTRIBUTIONS (3 s.h.)
This course is intended for students who are studying for the professional examination on Construction and Evaluation of Actuarial Models given by the Casualty Actuarial Society and the Society of Actuaries. It covers credibility models of insurance losses, simulation methods, and financial applications. It is a required course for all graduate students in actuarial science.
Prerequisites: 22S:154 or 22S:194; and a grade of C or higher in 22S:175; or consent of instructor.
Offered spring semesters.
Syllabus: Spring 2008 | Spring 2007
22S:180 MATHEMATICS OF FINANCE I (4 s.h.)
This course is intended for actuarial science majors who are studying for the professional exam on Financial Mathematics given by the Casualty Actuarial Society and the Society of Actuaries. The course concentrates on the theory of compound interest. Homework assignments are fairly intense. Major topics include the measurement of interest, annuities certain (level, non-level, and continuous), amortization schedules, sinking funds, yield rates, bonds, inflation, duration, immunzation, and an introduction to financial derivatives. Classes consist of lectures by a faculty member; students are given ample opportunity to ask questions. A basic knowledge of calculus and probability is assumed. Students' main activities are solving problems.
Prerequisites: 22M:026, and 22S:120 or 22S:130.
Offered fall and spring semesters.
Syllabus: Spring 2008 | Fall 2007 | Spring 2007
22S:181 LIFE CONTINGENCIES I (3 s.h.)
This course is an introduction to life insurance mathematics based on a stohastic approach. Major topics include life insurance, annuities, and benefit premiums. Classes consist of lectures. Grades are based on tests, quizzes, and homework. This is a required course for all students in actuarial science.
Prerequisites: 22S:153 or 22S:193; and grades of C or higher in 22S:174 and 22S:180.
Offered spring semesters.
Syllabus: Spring 2008 | Spring 2007
22S:182 LIFE CONTINGENCIES II (3 s.h.)
This is a continuation of 22S:181. Students are assumed to be proficient in calculus as covered in 22M:056. Development is based on a stochastic approach to life insurance models. Major topics include benefit premiums and reserves, and multi-life and multiple-decrement models. Classes consist of lectures by a faculty member; students are given ample opportunities to ask questions. This is a required course for all students in actuarial science.
Prerequisite: grade of C or higher in 22S:181.
Offered fall semesters.
Syllabus: Fall 2007
22S:183 MATHEMATICS OF FINANCE II (3 s.h.)
This course is intended for students who are studying for the professional examination on Actuarial Models: Financial Economics given by the Casualty Actuarial Society and the Society of Actuaries. It covers derivatives markets, interest rate models, and financial applications. It is a required course for all graduate students in actuarial science.
This course meets occasionally on Saturday mornings for exams.
Prerequisite: grade of C or higher in 22S:175
Offered fall semesters.
Syllabus: Fall 2007
22S:185 ASSET AND LIABILITY MANAGEMENT (3 s.h.)
Interest rate risk; immunization; duration analysis; cash flow matching; fundamental theorem of asset pricing; term structure of interest rate models.
Prerequisite: grade of C or higher in 22S:175 or 22S:181; or consent of instructor.
Offered spring semesters.
Syllabus: Spring 2007
22S:188 ACTUARIAL EXAM PREPARATION (arr.)
Repeatable: May be taken 4 times.
This course is designed to aid students in their preparation for the exams of the Society of Actuaries and the Casualty Actuarial Society. Each week problems from previous exams are assigned and are then worked a the next meeting. There are no official prerequisites for the course, but it is assumed that students have already studied (or are in the process of studying) the subjects tested on the exams. Typically, each section is devoted to particular exams. Graduate students in the Department of Statistics and Actuarial Science cannot use this course on their Plan of Study. Offered on an S-F basis only for undergraduates; instructor has the option of using S-U grades for Graduate College, School of Management, and graduate students in the College of Public Health.
22S:190 MATHEMATICAL METHODS FOR STATISTICS (3 s.h.)
Real numbers, point set theory, limit points, limits, sequences and series, Taylor series (multivariate), uniform convergence, Riemann-Stieltjes integrals.
Prerequisite: graduate standing in Statistics, or consent of instructor.
Offered spring semesters.
Syllabus: Spring 2008 | Spring 2007
22S:191 INDIVIDUAL STUDY (arr.)
Prerequisite: consent of advisor.
22S:193 STATISTICAL INFERENCE I (3 s.h.)
This is an intermediate-level course in mathematical statistics that comprises the first part of the 22S:193-194 sequence. The course attempts to establish many of the statistical concepts and structure upon which statistical inference is based. Concepts include probability, random variables, distributions, transformations and expectations, common families of distributions, multiple random variables, convergence concepts, and properties of a random sample. The majority of the statistical inference is accomplished in the next course, 22S:194.
Prerequisites: 22M:028 and 22S:131; or equivalents.
Offered fall semesters.
Syllabus: Fall 2007
22S:194 STATISTICAL INFERENCE II (3 s.h.)
This course is a continuation of 22S:193. It is intended for upper-level undergraduates and graduate students. The goal of this sequence is to impart to students a broad knowledge of the mathematical methods of statistical inference. Topics are similar to those covered in 22S:153-154, but are handled in more depth. Topics include sufficiency, the likelihood principle and other methods of estimation, likelihood ratio tests, most powerful tests, asymptotic theory, Bayesian inference, and interval estimation. Grades are determined on the basis of weekly homework and/or quizzes, midterms, and a final exam.
Prerequisite: 22S:193.
Offered spring semesters.
Syllabus: Spring 2008 | Spring 2007
22S:195 PROBABILITY AND STOCHASTIC PROCESSES I (3 s.h.)
This course provides students with an introduction to the theory of stochastic processes and probability models. Focus is on the theory and applications for Markov chains which include classification of states, basic limit theorem of Markov chains, branching processes, Markov Chain Monte Carlo (MCMC) methods (an important application of Markov chain theory and a hot topic in modern statistical analysis), and counting processes such as Poisson processes.
Prerequisite: 22S:130; or 22S:120 and consent of instructor.
Offered fall semesters.
Syllabus: Fall 2007
22S:196 PROBABILITY AND STOCHASTIC PROCESSES II (3 s.h.)
This course provides students with an introduction to Markov chains, covering enough theory to understand the performance of Markov chain Monte Carlo (MCMC) methods. The course will focus on the application of Markov chain theory to Monte Carlo calculations such as the Metropolis-Hasting algorithm and the Gibbs sampler. These methods will be applied to statistical settings which cannot be processed otherwise.
Prerequisite: 22S:195.
Offered spring semesters of odd years.
Syllabus: Spring 2007
22S:197 READINGS IN STATISTICS AND/OR ACTUARIAL SCIENCE (arr.)
Prerequisite: consent of instructor.
Primarily for Graduate Students
22S:203 FOUNDATIONS OF PROBABILITY I (3 s.h.)
Probability theory, with emphasis on constructing rigorous proofs; measure spaces, measurable functions, random variables and induced measures, distribution functions, Lebesque integral, product measure and independence, Borel Cantelli lemma, modes of convergence.
Prerequisite: 22S:190.
Offered fall semesters of odd years.
Syllabus: Fall 2007
22S:204 FOUNDATIONS OF PROBABILITY II (3 s.h.)
Laws of large numbers, characteristic functions and properties, central limit theorem, Radon-Nikodym derivatives, conditional expected value and martingales.
Offered spring semesters of even years.
Prerequisite: 22S:203.
Offered spring semesters of even years.
Syllabus: Spring 2008
22S:220 ANALYSIS OF CATEGORICAL DATA (3 s.h.)
Survey of theory and methods for categorical response and count data. Exact and approximate inference for contingency tables, logistic and Poisson regression, ordinal and multinomial logit models.
Prerequisites: 22S:194, or consent of instructor.
Same as 171:262.
Offered spring semesters.
Syllabus: Spring 2008 | Spring 2007
22S:225 SURVIVAL DATA ANALYSIS (3 s.h.)
Same as 171:261.
22S:235 TIME SERIES ANALYSIS (3 s.h.)
Stationary time series, ARIMA models, spectral representation, linear prediction inference for the spectrum, multivariate time series, state space models and processes, nonlinear time series.
Prerequisites: 22S:153, 22S:154, and 22S:156.
Offered fall semesters of odd years.
Syllabus: Fall 2007
22S:238 BAYESIAN ANALYSIS (3 s.h.)
Decision theory, coherence and utility, subjective probability, likelihood principle, conjugate families, structure of Bayesian inference, asymptotic approximations for posterior distributions, sequential experiments, exchangeability, hierarchical models, nonparametric Bayes procedures, empirical Bayes methods, numerical and Markov chain Monte Carlo methods.
Prerequisites: 22S:190 and 22S:194.
Offered fall semesters of odd years.
Syllabus: Fall 2007
22S:248 COMPUTER INTENSIVE STATISTICS (3 s.h.)
Computer arithmetic; random variate generation; numerical optimization; numerical differentiation, integration, and linear algebra; smoothing techniques; bootstrap methods; cross-validation; MCMC; EM and related algorithms; other topics per student/instructor interests.
Prerequisites: 22S:164 and proficiency in Fortran or C or C++.
Offered spring semesters.
Syllabus: Spring 2008 | Spring 2007
22S:253 ADVANCED INFERENCE I (3 s.h.)
Concepts of convergence, asymptotic methods including the delta method, sufficiency, asymptotic efficiency, Fisher information and information bounds for estimation, maximum likelihood estimation, the EM-algorithm, Bayes estimation, decision theory.
Prerequisites: 22S:190 and 22S:194.
Offered fall semesters of even years.
Syllabus:
22S:254 ADVANCED INFERENCE II (3 s.h.)
Hypothesis testing, asymptotics of the likelihood ratio test, asymptotic efficiency, statistical functionals, robustness, bootstrap and jackknife, estimation with dependent data.
Prerequisite: 22S:253.
Offered spring semesters of odd years.
Syllabus: Spring 2007 Spring 2007
