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# Courses in Statistics (Division 489)

Stat. 100. Introduction to Statistical Reasoning.
No credit granted to those who have completed or are enrolled in Soc. 210, Stat. 265, 311, 402, 405, or 412, or Econ. 404 or 405. (4). (MSA). (BS). (QR/1).
This course is designed to expose students to the basic ideas underlying statistical reasoning and modern statistical methodology. Topics covered include rudiments of probability theory, a critical discussion of alternative interpretations of probability, and gives the student an introduction to basic methods of statistical analysis.
Stat. 170. The Art of Scientific Investigation.
(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.
Stat. 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, 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 distribuitons (Normal Exponential, Weibull), point and interval estimation, likelihood functions, test of hypotheses for means, variances, and proportions for one and two populations.
Stat. 311/IOE 365. Engineering Statistics.
Engin. 101, Math. 215, and IOE 315 or Stat. 310. No credit granted to those who have completed or are enrolled in Stat. 265, 405, or 412, or Econ. 405. One credit granted to those who have completed Stat. 402. (4). (Excl). (BS). CAEN lab access fee required for non-Engineering students.
Collection and analysis of engineering data associated with stochastic industrial processes. Topics include: exploratory data analysis, describing relationships, importance of experimentation, applications of sampling distribution theory, test of hypotheses, experiments with one or more factors, and regression analysis. Students are required to use statistical packages on CAEN for problem solving.
Stat. 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. 265, 311, 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.
Stat. 403. Introduction to Statistics and Data Analysis II.
Stat. 402. (4). (Excl). (BS).
Continuation of Statistics 402. Additional topics in the design and analysis of experiments (partially hierarchical, Latin squares, split plot; fixed, random, and mixed models, both parametric and nonparametric techniques); multiple regression including some discussion of model choice and evaluation, partial correlations, multicollinearity, analysis of covariance; and analysis of categorical data from both a classical c2 perspective and via linear models. Each technique is presented with assumptions and illustrative examples.
Stat. 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 or 412. Students with credit for Econ. 404 can only elect Stat. 405 for 2 credits and must have permission of instructor. (4). (MSA). (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).
Stat. 406. Introduction to Statistical Computing.
Stat. 425 and 402. (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.
Stat. 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, or 405. One credit granted to those who have completed Stat. 402. (3). (MSA). (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.
Stat. 413. The General Linear Model and Its Applications.
Stat. 402 and Math. 217; concurrent enrollment in Stat. 425. Students who have not taken Math. 217 should elect Stat. 403. 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.
Stat. 414. Topics in Applied Statistics.
Stat. 413 or 403; prior or concurrent enrollment in Stat. 426; 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.
Stat. 425/Math. 425. Introduction to Probability.
Math. 215, 255, or 285. (3). (MSA). (BS).
Basic concepts of probability; expectation, variance, covariance; distribution functions; and bivariate, marginal, and conditional distributions.
Stat. 426. Introduction to Mathematical Statistics.
Stat. 425. (3). (MSA). (BS).
Treatment of experimental data, normal sampling theory, confidence intervals, and tests of hypotheses, and introduction to regression and analysis of variance. This course serves as a prerequisite for many 500-level statistics courses.
Stat. 430. Applied Probability.
Statistics 425. (3). (Excl).
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.
Stat. 466/IOE 466/Manufacturing 466. Statistical Quality Control.
Stat. 265 or 311. (3). (Excl). (BS). CAEN lab access fee required for non-Engineering students.
Design and analysis of procedures for forecasting and control of production processes. Topics include: attribute and variables sampling plans; sequential sampling plans; rectifying control procedures; charting, smoothing, forecasting, and prediction of discrete time series.
Stat. 470. Experimental Design.
Stat. 402. (4). (Excl). (BS).
Introduces students to basic principles in classical experimental design, including randomization, replication, confounding, interaction, covariates, use of the general linear model. Students are introduced to the following designs: completely randomized, randomized blocks, Latin squares, incomplete blocks, factorial, split plot, Taguchi, response surface, optimal.
Stat. 480. Survey Sampling Techniques.
Stat. 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.
Stat. 499. Honors Seminar.
Permission of departmental Honors advisor. (2-3). (Excl). (INDEPENDENT).
Stat. 500. Applied Statistics I.
Math. 417, and Stat. 402 or 426. (3). (Excl). (BS).
A review of matrices and multivariate normal and related distributions. Regression and general least squares theory, Gauss-Markov Theorem, estimation of regression coefficients, polynomial regression, step-wise regression, residuals, ANOVA models, multiple comparisons, analysis of covariance, Latin squares, 2p designs, and random and mixed effect models. Applications and real data analysis are stressed, with students using the computer to perform statistical analyses.
Stat. 501. Applied Statistics II.
Stat. 500. (3). (Excl). (BS).
Generalized linear models including logistics regression, Poisson regression, contingency tables. Analysis of survival data. Modern regression techniques. Regression and classification trees. Neural networks.
Stat. 502. Analysis of Categorical Data.
Stat. 426. (3). (Excl). (BS).
Models for contingency tables, including the Poisson, multinomial, and hypergeometric models; additive and log linear models for cell probabilities; estimation of parameters, exact and asymptotic sampling distributions, and sufficient statistics; tests of hypotheses, including likelihood ratio tests, chi-square tests, and Fisher's exact test; special topics, such as quantal response problems, incomplete tables, tests for trend, and/or measures of association.
Stat. 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.
Stat. 504. Seminar on Statistical Consulting.
Stat. 403 or 500. (3). (Excl). (BS). May be repeated for a total of eight credits.
Applications of statistics to problems in the sciences and social sciences; students are expected to analyze data and write reports.
Stat. 505/Econ. 673. Econometric Analysis.
Permission of instructor. (3). (Excl). (BS).
Theory and practice of hypothesis testing, statistical estimation, and the basic statistical theory underlying the linear model.
Stat. 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.
Stat. 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.
Stat. 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.
Stat. 526/Math. 526. Discrete State Stochastic Processes.
Math. 525/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.
Stat. 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.
Stat. 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.
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.
Stat. 560/Biostat. 685 (Public Health). 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.
Stat. 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.
Stat. 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.

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