# Courses in Statistics (Division 489)

300. Introduction to Statistical Reasoning. (3). (NS).

This course is designed to provide an overview of the field of statistics. Course topics include methods of analyzing and summarizing data, statistical reasoning as a means of learning from observations (experimental or sample), and techniques for dealing with uncertainties in drawing conclusions from collected data. Basic fallacies in common statistical analyses and reasoning are discussed and proper methods indicated. Alternative approaches to statistical inference are also discussed. The course emphasis is on presenting basic underlying concepts rather than on covering a wide variety of different methodologies. Evaluation is based upon a midterm and a final examination. The course format is lecture with some discussion.

402. Introduction to Statistics and Data Analysis. No credit granted to those who have completed 412. (4). (NS).

In this course students are introduced to the concepts and applications of statistical methods and data analysis. Statistics 402 has no prerequisite and has been elected by students whose mathematics background includes only high school algebra. Examples of applications are drawn from virtually all academic areas and some attention is given to statistical process control methods. The course format includes three lectures and a laboratory (l.5 hours per week). The laboratory section covers some of the data analysis material and introduces the use of interactive computing through the use of MIDAS. Course evaluation is based on a combination of three examinations GIVEN WEDNESDAY EVENINGS, a final examination and teaching fellow input.

403. Introduction to Statistics and Data Analysis II. Stat. 402. (4). (NS).

BASICS OF SURVEY SAMPLING. The course will survey the primary sampling designs and analysis of survey data. Topics include: stratified sampling, cluster sampling, multistage sampling, non-response, response bias and error and ratio estimation. APPLIED REGRESSION. The course will also cover various topics associated with the general linear model emphasizing applications. Topics include: multiple regression, variable selection, stepwise regression, residual analysis, analysis of variance models, covariance analysis and principal components. OTHER TOPICS. As time allows, the course may cover some aspects of probit and logit analyses, analysis of time series data, reliability analysis, and topics in experimental design. Three hours of lecture and one and one-half hours of lab per week.

405/Econ. 405. Introduction to Statistics. Math. 115 or permission of instructor. Juniors and seniors may elect concurrently with Econ. 201 and 202. No credit granted to those who have completed Econ. 404. (4). (SS).

See Economics 405. (Thursby)

412. Introduction to Probability and Statistics. Prior or concurrent enrollment in Math. 215 and either CS 283 or Engin. 102. No credit granted to those who have completed 311 or 402. (3). (NS).

The objectives of this course are to introduce students to the basic ideas of probability and statistical inference and to acquaint students with some important data analytic techniques, such as regression and the analysis of variance. Examples will emphasize applications to the natural sciences and engineering. There will be regular homework, including assignments which require the use of MTS, two midterms, and a final exam.

425/Math. 425. Introduction to Probability. Math. 215. (3). (N.Excl).

See Math 425.

426. Introduction to Mathematical Statistics. Stat. 425. (3). (NS).

This course covers the basic ideas of statistical inference, including sampling distributions, estimation, confidence intervals, hypothesis testing, regression, analysis of variance, nonparametric testing, and Bayesian inference. The sequence of Statistics 425/426 serves as a prerequisite for more advanced Statistics courses. Weekly problem sets, two hourly exams, and one final exam.

466/IOE 466. Statistical Quality Control. Statistics 311 or IOE 365. (3). (Excl).

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.

470. The Art of Scientific Investigation. Stat. 402 or 412 or equivalent. (4). (N.Excl).

The objective of this course is to introduce students to the process of planning, designing and implementation of a study. Includes enumerative, Monte Carlo, observational and controlled randomized experimentation. Emphasis is on the conceptual framework not on the mathematical theory of design (e.g., Statistics 570). (Rothman)

502. Analysis of Categorical Data. Stat. 426. (3). (NS).

Models for contingency tables, including the Poisson, multinomial, and hypergeometric models; additive and loglinear models for cell probabilities; estimation of parameters, exact and asymptotic sampling distributions, and sufficient statistics, tests of hypotheses, including likelihood ratio tests.

504. Seminar on Statistical Consulting. Stat. 403 or 500. (1-4). (Excl). May be repeated for a total of 8 credits.

Applications of statistics to problems in the sciences and social sciences; students will be expected to analyze data and write reports.

510/Math. 525. Probability Theory. Math. 450 or 451; or permission of instructor. Students with credit for Math. 425/Stat. 425 can elect Math. 525/Stat. 510 for one credit. (3). (N.Excl).

See Math 525.

511. Mathematical Statistics. Stat. 510 or Math. 525; or permission of instructor. (3). (N.Excl).

Topics in Mathematical Statistics will include: Introduction to decision theory, estimation, sufficiency, completeness, maximum likelihood, and Bayes estimators, interval estimation UMP tests, unbiased tests and introductions to the analysis of variance and regression. (Muirhead)

526/Math. 526/C.I.C.E. 516. Discrete State Stochastic Processes. Math. 525; or Stat. 510; or C.I.C.E. 512. (3). (N.Excl).

Review of discrete distributions, generating functions, compound distributions, renewal theorem, systems as Markov chains. Properties of Markov chains: Chapman-Kolmogorov equations, return and first passage times, classification of states and periodicity, absorption probabilities, forward equations, stationary distributions, backward equation, ergodicity, limit properties. Branching and queueing processes: examples from engineering, biological and social sciences; continuous time Markov chains, embedded chains, the M/G/1 queue, Markovian decision processes, inventory problems.

531. Statistical Analysis of Time Series. Stat. 426. (3). (NS).

The major topics include time- and frequency-domain characteristics of stationary discrete time series, autoregressive and moving average models, prediction theory, estimation and hypothesis testing, and computer applications. Special topics might include vector autoregression, cross-spectral analysis, causality testing or other issues of current interest. Statistics 511 or Economics 775 is the standard prerequisite. Student evaluation is based on exams, homework, and a term paper. Lectures and problem sets including computer exercises are the main methods of instruction. (Howrey)

570. Experimental Design. Stat. 426 and a basic knowledge of matrix algebra; or permission of instructor. (3). (NS).

Basic topics and ideas in the design of experiments: randomization and randomization tests; the validity and analysis of randomized experiments; randomized blocks; Latin and Graeco-Latin squares; plot techniques; factorial experiments; the use of confounding and response surface methodology; weighing designs, lattice and incomplete block and partially balanced incomplete block designs.

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