# Mathematics and Statistics

## College of Natural Sciences and Mathematics

### Mathematics and Statistics - STAT Courses

#### Statistics Courses (STAT)

380. Probability and Statistics (3)
Prerequisites: MATH 222 or 224.
Frequency interpretation of probability. Axioms of probability theory. Discrete probability and combinatorics. Random variables. Distribution and density functions. Moment generating functions and moments. Sampling theory and limit theorems.
Letter grade only (A-F). (Lecture 3 hrs.) Same course as MATH 380.

*381. Mathematical Statistics (3)
Prerequisites: MATH 247, and MATH 380 or STAT 380.
Estimation and hypothesis testing. Maximum likelihood and method of moments estimation. Efficiency, unbiasedness, and asymptotic distribution of estimators. Neyman-Pearson Lemma. Goodness-of-fit tests. Correlation and regression. Experimental design and analysis of variance. Nonparametric methods.
Letter grade only (A-F). (Lecture 3 hrs.) Not open for credit to students with credit in MATH 381.

410./510. Regression Analysis (3)
Prerequisites: MATH 247 and MATH/STAT 380, prerequisite or corequisite STAT 381. (Undergraduates enroll in STAT 410; graduates enroll in STAT 510.)
Simple linear regression: estimation and inference, prediction, analysis of residuals, detection of outliers, use of transformations. Multiple linear regression: influence diagnostics, multi-collinearity, selection of variables, simultaneous estimation and inference, validation techniques. Statistical software for data analysis used.
Letter grade only (A-F). (Lecture 3 hrs.) Not open for credit to students with credit in MATH 480 or 590.

450./550. Multivariate Statistical Analysis (3)
Prerequisites: STAT 381, prerequisite or corequisite STAT 410. (Undergraduates register in STAT 450; graduates enroll in STAT 550.)
Discriminate analysis, principal components, factor analysis, cluster analysis, logistic regression, canonical correlation, multidimensional scaling, and some nonlinear techniques. Statistical software used.
Letter grade only (A-F). (Lecture 3 hrs.) Not open for credit to students with credit in MATH 483 or 593.

*475. Data Analysis with SAS (3)
Prerequisites: STAT 381 or consent of instructor.
Topics include: Statistical analysis including extraction, presentation of data in graphical form, creation, modification of datasets, interpretation of output, writing of reports. Provides SAS programming techniques for aforementioned topics preparation for SAS base certification.
Letter grade only (A-F). (Lecture 3 hrs.) Not open for credit to students with credit in MATH 489.

*482. Random Processes (3)
Prerequisites: MATH 247, and MATH 380 or STAT 380.
Further topics in probability. Markov processes. Renewal theory. Random walks. Queueing theory. Poisson processes. Brownian motion.
Letter grade only (A-F). (Lecture 3 hrs.) Not open for credit to students with credit in MATH 382.

*484. Actuarial Science: Models (3)
Prerequisites: STAT 381 or consent of instructor.
Statistical techniques applied to risk management. Expected utility theory, individual risk models, compound Poisson distributions and processes, ruin probability and first surplus, stop-loss and proportional reinsurance, statistical survival distributions and life tables, life annuity, actuarial present values, and premiums determination.
Letter grade only (A-F). (Lecture 3 hrs.) Not open for credit to students with credit in MATH 484.

*485. Actuarial Science: Financial Mathematics (3)
Prerequisites: STAT 381.
Simple and compound interests, stochastic approaches to interest and annuities, stochastic models of stock, Black-Scholes arbitrage pricing of options and other derivative securities, Markowitz portfolio optimization theory, Ito financial calculus, filtrations and martingales.
Letter grade only (A-F). (Lecture 3 hrs.)

495./595. Topics in Modern Statistics (3)
Prerequisites: Consent of instructor.
Topics of current interest from statistics literature.
Letter grade only (A-F). Course may be repeated to a maximum of 6 units with different topics. (Lecture 3 hrs)

497. Directed Studies (1-3)
Prerequisites: Consent of instructor.
Junior or senior standing and consent of instructor. Not open to graduate students.

510./410. Regression Analysis (3)
Prerequisites: MATH 247 and 380, prerequisite or corequisite STAT 381. (Undergraduates enroll in STAT 410; graduates enroll in STAT 510.)
Simple linear regression: estimation and inference, prediction, analysis of residuals, detection of outliers, use of transformations. Multiple linear regression: influence diagnostics, multi-collinearity, selection of variables, simultaneous estimation and inference, validation techniques. Statistical software for data analysis used.
Letter grade only (A-F). (Lecture 3 hrs.) Not open for credit to students with credit in MATH 480 or 590.

520. Statistical Inference (3)
Prerequisites: STAT 381 or consent of instructor.
Properties of a random sample, convergence in probability, law of large numbers, sampling from the normal distribution, the central limit theorem, principles of data reduction, likelihood principle, point estimation, Bayesian estimation, methods of evaluating estimators, hypothesis testing, decision theory, confidence intervals.
Letter grade only (A-F). (Lecture 3 hrs.) Not open for credit to students with credit in MATH 580.

530. Experimental Design (3)
Prerequisites: STAT 381 or consent of instructor.
Design of experiments to permit efficient analysis of sources of variation with application to quality assurance. Factorial and fractional factorial designs; block designs; confounding. Fixed and random effect models. Effects of departure from assumptions; transformations. Response surface techniques. Taguchi methods.
Letter grade only (A-F). (Lecture 3 hrs.) Not open for credit to students with credit in MATH 581.

532. Statistical Quality Control (3)
Prerequisites: STAT 381 or consent of instructor.
Introduction to methods of statistical quality control. Includes control charts, acceptance sampling, process capability analysis, and aspects of experimental design.
Letter grade only (A-F). (Lecture 3 hrs.) Not open for credit to students with credit in MATH 584.

540. Survey Sampling (3)
Prerequisites: STAT 381 or consent of instructor.
Theory and practice of sampling from finite populations. Simple random sampling, stratified random sampling, systematic sampling, cluster sampling, properties of various estimators including ratio, regression, and difference estimators. Error estimation for complex samples.
Letter grade only (A-F). (Lecture 3 hrs.) Not open for credit to students with credit in MATH 583.

550./450. Multivariate Statistical Analysis (3)
Prerequisites: STAT 381, prerequisite or corequisite STAT 410. (Undergraduates register in STAT 450; graduates enroll in STAT 550.)
Discriminate analysis, principal components, factor analysis, cluster analysis, logistic regression, canonical correlation, multidimensional scaling, and some nonlinear techniques. Statistical software used.
Letter grade only (A-F). (Lecture 3 hrs.) Not open for credit to students with credit in MATH 483 or 593.

560. Nonparametric Statistics (3)
Prerequisites: STAT 410, or 510, or consent of instructor.
Alternatives to normal-theory statistical methods, analysis of categorical and ordinal data, methods based on ranks, measures of association, goodness of fit tests, order statistics.
Letter grade only (A-F). (Lecture 3 hrs.) Not open for credit to students with credit in MATH 585.

570. Statistical Simulation (3)
Prerequisites: STAT 381 or consent of instructor.
Simulation modeling techniques; generation of discrete and continuous random numbers from given distributions; Monte Carlo methods; discrete event simulations, statistical analysis of simulated data; variance reduction; statistical validation; introduction to simulation languages; industry applications. Statistical packages used.
Letter grade only (A-F). (Lecture 3 hrs.) Not open for credit to students with credit in MATH 587 or 487.

572. Computational Statistics (3)
Prerequisites: STAT 381 or consent of instructor.
Random number generation, sampling and subsampling, exploratory data analysis, Markov chain Monte Carlo methods, density estimation and EM algorithm. Topics of current interest.
Letter grade only (A-F). (Lecture 3 hrs.)

574. Data Mining (3)
Prerequisites: STAT 410, or 510, or consent of instructor.
Basics of data mining algorithms with emphasis on industrial applications. Prediction and classification techniques such as decision trees, neural networks, Multivariate Adaptive Regression Splines, and other methods. Several software packages utilized. Letter grade only (A-F). (Lecture 3 hrs.) Not open for credit to students with credit in MATH 586.

576. Data Informatics (3)
Prerequisites: STAT 410/510 or consent of instructor.
Genetic algorithms, fuzzy logic, discrete choice analysis, online analytical processing, structured query language, statistical database management, and text and web mining. Topics of current interest.
Letter grade only (A-F). (Lecture 3 hrs).

580. Time Series (3)
Prerequisites: STAT 381 or consent of instructor.
Includes moving averages, smoothing, Box-Jenkins (ARIMA) models, testing for nonstationarity, model fitting and checking, prediction and model selection, seasonal adjustment, ARCH, GARCH, cointegration, state-space models. Statistical packages used throughout the course.
Letter grade only (A-F). (Lecture 3 hrs.) Not open for credit to students with credit in MATH 582.

590. Statistical Analysis of Medical Data (3)
Prerequisites: STAT 381 or consent of instructor.
Lifetime distributions, hazard and survival functions, censoring and truncation, Kaplan Meier and Nelson-Aelen estimators, Cox proportional hazard models, m-sample tests, goodness-of-fit tests, Bayesian survival analysis, analysis of multivariate survival data, exploring longitudinal data designs and models, clinical trials.
Letter grade only (A-F). (Lecture 3 hrs.)

595./495. Topics in Modern Statistics (3)
Prerequisites: Consent of instructor.
Topics of current interest from statistics literature.
Letter grade only (A-F). Course may be repeated to a maximum of 6 units with different topics. (Lecture 3 hrs)

695. Seminar in Applied Statistics (3)
Prerequisites: Consent of instructor.
Presentation and discussion of advanced work in applied statistics.
May be repeated to a maximum of six units. Letter grade only (A-F).

697. Directed Studies in Applied Statistics (1-3)
Prerequisites: Consent of instructor.
Research on a specific area in applied statistics. Topic for study to be approved and directed by a statistics faculty member.