01-02 LS&A Bulletin

Courses in Statistics (Division 489)

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STATS 100. Introduction to Statistical Reasoning.: No credit granted to those who have completed or are enrolled in Soc. 210, Stat. 350, 350, 402, 405, or 412, or Econ. 404 or 405. (4). (MSA). (BS). (QR/1).; Provides an overview of the field of statistics, including methods of summarizing and analyzing data, statistical reasoning for learning from observations (experimental or sample), and techniques for dealing with uncertainties in drawing conclusions from collected data. Emphasis is on presenting underlying concepts rather than covering a variety of different methodologies.
STATS 125. Games, Gambling and Coincidences.: Only first-year students, including those with sophomore standing, may pre-register for First-Year Seminars. All others need permission of instructor. (3). (MSA). (QR/1).; Emphasizes problem solving and modeling related to games, gambling and coincidences, touching on many fundamental ideas in discrete probability, finite Markov chains, dynamic programming and game theory.
STATS 170. The Art of Scientific Investigation.: No credit granted to those who have completed or are enrolled in Statistics 408. (4). (MSA). (BS). (QR/1).; This course explores the critical thought processes involved in a scientific investigation. Concepts covered include: the role of empiricism, modeling, the nature of variability, the design of scientific experiments (advantages and disadvantages), the role of randomization, the measurement process, possible biases, the use of controls, and the evaluation of final results. Examples from the history of science are used to illustrate successes and failures in science and various ethical issues are considered.
STATS 265 / IOE 265. Probability and Statistics for Engineers.: Math. 116 and Engin. 101. No credit granted to those who have completed or are enrolled in Stat. 311, 400, 405, or 412, or Econ. 405. (4). (Excl). (BS). CAEN lab access fee required for non-Engineering students.; Graphical representation of data; axioms of probability; conditioning, Bayes Theorem; discrete distributions (geometric, binomial, Poisson); continuous distributions (Normal Exponential, Weibull), point and interval estimation, likelihood functions, test of hypotheses for means, variances, and proportions for one and two populations.
STATS 350(250/402). Introduction to Statistics and Data Analysis.: No credit granted to those who have completed or are enrolled in Econ. 404 or 405, or Stat. 350, 265, 311, 400, 402, 405, or 412. (4). (NS). (BS). (QR/1).; A one term course in applied statistical methodology from an analysis-of-data viewpoint. Frequency distributions; measures of location; mean, median, mode; measures of dispersion; variance; graphic presentation; elementary probability; populations and samples; sampling distributions; one sample univariate inference problems, and two sample problems; categorical data; regression and correlation; and analysis of variance. Use of computers in data analysis. Three hours lecture and one and one-half hour laboratory session each week.
STATS 400. Applied Statistical Methods.: High School Algebra. No credit granted to those who have completed or are enrolled in Econ. 404 or 405, or Stat. 350, 350, 265, 402, 405, or 412. (4). (Excl). (BS).; Statistics and the scientific method; observational study versus designed experiment; visualization; introduction to probability; statistical inference; confidence intervals; one-sample tests of hypothesis; two-sample problems; analysis of variance (ANOVA); blocked designs; tests for association and independence (chi-square tests); regression and correlation; and non-parametric tests.
STATS 401(403). Applied Statistical Methods II.: Stat. 350. (4). (Excl). (BS).; An intermediate course in applied statistics, covering a range of topics in modeling and analysis of data including: review of simple linear regression, two-sample problems, one-way analysis of variance; multiple linear regression, diagnostics and model selection; two-way analysis of variance, multiple comparisons, and other selected topics.
STATS 405 / ECON 405. Introduction to Statistics.: Math. 116 or 118. Juniors and seniors may elect this course concurrently with Econ. 101 or 102. No credit granted to those who have completed or are enrolled in Stat. 265, 311, 400 or 412. Students with credit for Econ. 404 can only elect Stat. 405 for 2 credits and must have permission of instructor. (4). (Excl). (BS). (QR/1).; The purpose of this course is to provide students with an understanding of the principles of statistical inference. Topics include probability, experimental and theoretical derivation of sampling distributions, hypothesis testing, estimation, and simple regression. (Students are advised to elect the sequel, Economics 406).
STATS 406. Introduction to Statistical Computing.: One of Stat. 205 (or 402), 405, 412, or 425. (4). (Excl). (BS).; Selected topics in statistical computing, including basic numerical aspects, iterative statistical methods, principles of graphical analyses, simulation and Monte Carlo methods, generation of random variables, stochastic modeling, importance sampling, numerical and Monte Carlo integration.
STATS 408. Statistical Principles for Problem Solving: A Systems Approach.: High School Algebra. No credit granted to those who have completed or are enrolled in Statistics 170. (4). (Excl). (BS).; Our purpose is to help you use quantitative reasoning to facilitate learning. Specifically, we introduce statistical and mathematical principles, and then use these as analogues in a variety of real world situations. The notion of a system, a collection of components that come together repeatedly for a purpose, provides an excellent framework to describe many real world phenomena and provides a way to view the quality of an inferential process.
STATS 412. Introduction to Probability and Statistics.: Prior or concurrent enrollment in Math. 215 and CS 183. No credit granted to those who have completed or are enrolled in Econ. 405, or Stat. 265, 311, 350, 400, or 405. One credit granted to those who have completed Stat. 350 or 402. (3). (Excl). (BS).; An introduction to probability theory; statistical models, especially sampling models; estimation and confidence intervals; testing statistical hypotheses; and important applications, including the analysis of variance and regression.
STATS 413. The General Linear Model and Its Applications.: Stat. 350 (or 402) and Math. 217; concurrent enrollment in Stat. 425. Students who have not taken Math. 217 should elect Stat. 401. Two credits granted to those who have completed Stat. 403. (4). (Excl). (BS).; Introduces students to the general linear model and its assumptions, and covers such topics as the geometry of the model, projections, least squares estimation, residuals, normal distribution theory results, inference on parameters, diagnostic tools, and applications in analysis of variance, design, and time series.
STATS 414. Topics in Applied Statistics.: Stat. 413 or 401; and permission of instructor. (4). (Excl). (BS).; Topics in applied statistics, including random and mixed effects ANOVA models, analysis of covariance and repeated measures designs, ridge regression, splines, logit-probit analysis, log-linear models, topics in multivariate analysis (MANOVA, discriminant analysis, profile analysis) topics in time series analysis, and basics of survival analysis.
STATS 425 / MATH 425. Introduction to Probability.: Math. 215, 255, or 285. (3). (Excl). (BS).; Basic concepts of probability; expectation, variance, covariance; distribution functions; and bivariate, marginal, and conditional distributions.
STATS 426. Introduction to Theoretical Statistics.: Stat. 425. (3). (Excl). (BS).; An introduction to theoretical statistics for students with a background in probability. Probability models for experimental and observational data, normal sampling theory, likelihood-based and Bayesian approaches to point estimation, confidence intervals, tests of hypotheses, and an introduction to regression and the analysis of variance.
STATS 430. Applied Probability.: Stats. 425. (3). (Excl). (BS).; Review of probability theory; introduction to random walks; counting and Poisson processes; Markov chains in discrete and continuous time; equations for stationary distributions; introduction to Brownian motion. Selected applications such as branching processes, financial modeling, genetic models, the inspection paradox, inventory and queuing problems, prediction, and/or risk analysis.
STATS 466 / IOE 466 / MFG 466. Statistical Quality Control.: Stat. 265 and Stat 401 or IOE 366. (4). (Excl). (BS). CAEN lab access fee required for non-Engineering students.; Quality improvement philosophies; Modeling process quality, Statistical process control, Control charts for variables and attributes, CUSUM and EWMA, Short production runs, Multivariate quality control, Auto correlation, Engineering process control, Economic design of charts, Fill control, Precontrol, Adaptive schemes, Process capability, Specifications and tolerances, Gage Capability studies, Acceptance Sampling by attributes and variables, International quality standards.
STATS 470. Introduction to the Design of Experiments.: Stat. 350. (4). (Excl). (BS).; Introduces students to basic concepts for planning experiments and to efficient methods of design and analysis. Topics covered include concepts such as randomization, replication and blocking; analysis of variance and covariance and the general linear model; factorial and fractional factorial designs, blocked designs, and split-plot designs.
STATS 480. Survey Sampling Techniques.: Stat. 350 (or 402). (4). (Excl). (BS).; Introduces students to basic ideas in survey sampling, moving from motivating examples to abstraction to populations, variables, parameters, samples and sample design, statistics, sampling distributions, Horvitz-Thompson estimators, basic sample design (simple random, cluster, systematic, multiple stage), various errors and biases, special topics.
STATS 499. Honors Seminar.: Permission of departmental Honors advisor. (2-3). (Excl). (INDEPENDENT).; Advanced topics, reading and/or research in applied or theoretical statistics.
STATS 500. Applied Statistics I.: Math. 417, and Stat. 350 (or 402) or 426. (3). (Excl). (BS).; Linear models: definitions, fitting, identifiability, collinearity, Gauss-Markov theorem, variable selection, transformation, diagnostics, outliers and influential observations. ANOVA and ANCOVA. Common Designs. Applications and real data analysis are stressed, with students using the computer to perform statistical analyses.
STATS 501. Applied Statistics II.: Stat. 500. (3). (Excl). (BS).; Generalized linear models including logistics regression, Poisson regression, contingency tables. Random effects and repeated measures. Modern regression techniques. Regression and classification trees. Neural networks.
STATS 503. Applied Multivariate Analysis.: Stat. 500. (3). (Excl). (BS).; Topics in applied multivariate analysis including Hotelling's T-squared, multivariate ANOVA, discriminant functions, factor analysis, principal components, canonical correlations, and cluster analysis. Selected topics from: maximum likelihood and Bayesian methods, robust estimation and survey sampling. Applications and data analysis using the computer is stressed.
STATS 504. Statistical Consulting.: Stat. 401 or 500. (3). (Excl). (BS). May be elected for a total of nine credits.; Introduces students to key aspects of statistical consulting and data analysis activities. Problem solving and real applications; data analysis, reports, presentations.
STATS 505 / ECON 671. Econometric Analysis I.: Permission of instructor. (3). (Excl). (BS).; Econ 673 and 674 form the basic required sequence in econometrics for all doctoral students. Their purpose is to provide Ph.D. students with the training needed to do the basic quantitative analysis generally understood to be part of the background of all modern economists. This includes: the theory and practice of testing hypotheses, statistical estimation theory, the basic statistical theory underlying the linear model, an introduction to econometric methods, and the nature of the difficulties which arise in applying statistical procedures to economic research problems.
STATS 510. Mathematical Statistics I.: Math. 450 or 451, and a course in probability or statistics. (3). (Excl). (BS).; Review of probability theory including: probability, conditioning, independence, random variables, standard distributions, exponential families, inequalities and a central limit theorem. Introduction to decision theory including: models, parameter spaces, decision rules, risk functions, Bayes versus classical approaches, admissibility, minimax rules, likelihood functions and sufficiency. Estimation theory including unbiasedness, complete sufficient statistics, Lehmann-Scheffe and Rao-Blackwell theorems, and various types of estimators.
STATS 511. Mathematical Statistics II.: Stat. 510. (3). (Excl). (BS).; More on the theory of estimation including: minimax, Bayes and James-Stein estimators. The theory of hypothesis testing including: tests significance levels, power, the Neyman-Pearson lemma, uniformly most powerful unbiased tests, monotone likelihood ratios, locally best tests, similar tests, likelihood ratio tests and the associated large sample theory, sequential tests, goodness of fit tests, and tests in contingency tables. Other topics include: confidence regions, introduction to the general linear model, and non-parametric methods.
STATS 525 / MATH 525. Probability Theory.: Math. 450 or 451. Students with credit for Math. 425/Stat. 425 can elect Math. 525/Stat. 525 for only one credit. (3). (Excl). (BS).; Axiomatic probability; combinatorics; random variables and their distributions; special distributions; joint, marginal and conditional distributions; expectation; the mean, variance, and moment generating function; induced distributions; sums of independent random variables; the law of large numbers; the central limit theorem. Optional topics drawn from: random walks, Markov chains, and/or martingales.
STATS 526 / MATH 526. Discrete State Stochastic Processes.: Stat. 525 or EECS 501. (3). (Excl). (BS).; Review of discrete distributions; generating functions; compound distributions, renewal theorem; modeling of systems as Markov chains; Markov chains: first properties; Chapman-Kolmogorov equations; return and first passage times; classification of states and periodicity; absorption probabilities and the forward equation; stationary distributions and the backward equation; ergodicity; limit properties; application to branching and queueing processes; examples from engineering, biological, and social sciences; Markov chains in continuous time; embedded chains; the M/G/1 queue; Markovian decision processes; application to inventory problems; other topics at instructor's discretion.
STATS 531 / ECON 677. Analysis of Time Series.: Stat. 426. (3). (Excl). (BS).; Decomposition of series; trends and regression as a special case of time series; cyclic components; smoothing techniques; the variate difference method; representations including spectrogram, periodogram, etc.; stochastic difference equations, autoregressive schemes, moving averages; large sample inference and prediction; covariance structure and spectral densities; hypothesis testing and estimation and applications and other topics.
STATS 535 / IOE 562. Reliability.: Stat. 425 and 426 (or IOE 316 and 366). (3). (Excl). (BS). CAEN lab access fee required for non-Engineering students.; This course covers the important reliability concepts and methodology that arise in modeling, assessing, and improving product reliability and in analyzing field and warranty data. Topics are selected from the following: Basic reliability concepts; Common parametric models for component reliability; Censoring schemes; Analysis of time-to-failure data; Accelerated testing for reliability assessment; Modeling and analyzing repairable systems reliability; Analysis of warranty and field-failure data; Maintenance policies and availability; Reliability improvement through experimentation.
STATS 550 / IOE 560 / SMS 576. Bayesian Decision Analysis.: Stat. 425. (3). (Excl). (BS). CAEN lab access fee required for non-Engineering students.; Axiomatic foundations for personal probability and utility; interpretation and assessment of personal probability and utility; formulation of Bayesian decision problems; risk functions, admissibility; likelihood principle and properties of likelihood functions; natural conjugate prior distributions; improper and finitely additive prior distributions; examples of posterior distributions, including the general regression model and contingency tables; Bayesian credible intervals and hypothesis tests; applications to a variety of decision-making situations.
STATS 560 / BIOSTAT 685. Introduction to Nonparametric Statistics.: Stat. 426. (3). (Excl). (BS).; Confidence intervals and tests for quantiles, tolerance regions, and coverages; estimation by U statistics and linear combination or order statistics; large sample theory for U statistics and order statistics; the sample distribution and its uses including goodness-of-fit tests; rank and permutation tests for several hypotheses including a discussion of locally most powerful rank and permutation tests; and large sample and asymptotic efficiency for selected tests.
STATS 575 / ECON 775. Econometric Theory I.: Math. 417 and 425 or Econ. 653, 654, 673, and 674. (3). (Excl). (BS).; A course in econometric theory stressing the statistical foundations of the general linear model. The course involves a development of the required theory in mathematical statistics; and derivations and proofs of main results associated with statistical inference in the general linear model.
STATS 576 / ECON 776. Econometric Theory II.: Stat. 575. (3). (Excl). (BS).; Generalized least squares, multivariate multiple regression, simultaneous equation models (including problems of identification, estimation by equation and system methods, and forecasting), introduction to asymptotic theory, and estimation problems in time series models.

Graduate Course Listings for STATS.

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