# Statistics

STAT 1342 (MATH 1342) Statistical Decision Making (3 semester credit hours) Principles of quantitative decision making: summarizing data, modeling uncertainty, loss functions, probability, conditional probability, random variables. Introduction to statistics: estimation, confidence intervals, hypothesis testing, regression. Introduction to statistical packages. May not be used to satisfy degree requirements for majors in the School of Engineering and Computer Science, or major requirements in the Schools of Management or Natural Sciences and Mathematics. Prerequisite: MATH 1306 or MATH 1314 or equivalent. (3-0) S (2015-04-18 11:40:20)

STAT 2332 Statistics for Life Sciences (3 semester credit hours) Graphs, histograms, mean, median, standard deviation, Chebyshev's inequality, standardized scores, simple linear regression and correlation; basic rules of probability, Bayes theorem; Normal t, chi squared, F, binomial and Poisson distributions; point estimation; hypothesis tests and confidence intervals for means, proportions regression coefficients, and correlation; one way ANOVA; contingency tables. Applications in life sciences will be emphasized throughout the course. May not used to satisfy degree requirements for mathematics, engineering, or computer science majors. Prerequisite: MATH 2312 or MATH 1325 or MATH 2413 or MATH 2414 or MATH 2417 or MATH 2419 or equivalent. (3-0) S (2015-04-18 11:40:20)

STAT 3103 Statistical Computer Packages (1 semester credit hour) An introduction to the use of statistics packages, such as SAS, BMD, SPSS, Minitab, and S, for the analysis of data. Based primarily on self-study materials. May not used to satisfy degree requirements for mathematics majors. Prerequisites: one semester of statistics and instructor consent required. (1-0) S (2015-04-18 11:40:20)

STAT 3332 Statistics for Life Sciences (3 semester credit hours) Graphs, histograms, mean, median, standard deviation, Chebyshev's inequality, standardized scores, simple linear regression and correlation; basic rules of probability, Bayes theorem; Normal t, chi squared, F, binomial and Poisson distributions; point estimation; hypothesis tests and confidence intervals for means, proportions regression coefficients, and correlation; one way ANOVA; contingency tables. Applications in life sciences will be emphasized throughout the course. May not used to satisfy degree requirements for mathematics, engineering, or computer science majors. This course will retain core notation for a transition period - see http://go.utdallas.edu/core-curriculum-transition. Please consult advisors for more detailed information. Prerequisite: MATH 2312 or MATH 1325 or equivalent. (3-0) S (2015-04-18 11:40:20)

STAT 3341 Probability and Statistics in Computer Science and Software Engineering (3 semester credit hours) Axiomatic probability theory, independence, conditional probability. Discrete and continuous random variables, special distributions of importance to CS/SE, and expectation. Simulation of random variables and Monte Carlo methods. Central limit theorem. Basic statistical inference, parameter estimation, hypothesis testing, and linear regression. Introduction to stochastic processes. Illustrative examples and simulation exercises from queuing, reliability, and other CS/SE applications. Credit cannot be received for both courses, (CS 3341 or SE 3341 or STAT 3341) and ENGR 3341. Prerequisites: (MATH 1326 or MATH 2414 or MATH 2419), and (CE 2305 or CS 2305 or TE 2305 with a grade of C or better). (Same as CS 3341 and SE 3341) (3-0) S (2015-04-18 11:40:20)

STAT 3355 Data Analysis for Statisticians and Actuaries (3 semester credit hours) Methods of data analysis used in different areas of Statistics and Actuarial Science. Sampling, fitting and testing models, regression, and comparison of populations. A statistical computer package will be used. Prerequisite: MATH 2415 or MATH 2419. (3-0) Y (2015-04-18 11:40:20)

STAT 3360 Probability and Statistics for Management and Economics (3 semester credit hours) Probability theory including independence, conditioning, density functions, frequently used families of distributions, random variables, expectation, moments, and the central limit theorem; statistical inference including sampling, estimation, hypothesis testing, and regression. May not used to satisfy degree requirements for mathematics, engineering, or computer science majors. Prerequisite: MATH 1326. (3-0) S (2015-04-18 11:40:20)

STAT 4351 Probability (3 semester credit hours) Sample spaces, probability of events, Kolmogorov's axioms, independence and dependence, Bayesian methodology. Discrete and continuous random variables. Probability distributions, mass functions and densities of univariate and multivariate random variables. Expected values, variances, moment generating functions, covariances and related issues. Probability inequalities. Special probability distributions and special probability densities. Functions of random variables, distribution function techniques, transformation techniques for one and several variables, moment-generating techniques. The law of large numbers, the central limit theorem and classical sampling distributions. Proofs of all main results. Practical examples illustrating the theory. The course can be used as a preparation for the first (Probability) actuarial exam. Prerequisite: MATH 2451. (3-0) Y (2015-04-18 11:40:20)

STAT 4352 Mathematical Statistics (3 semester credit hours) Sampling distributions. Order statistics. Decision theory including minimax and Bayes criterion. Point estimation including unbiased estimators, efficiency, consistency, sufficiency, robustness, the method of moments, the method of maximum likelihood, Bayesian estimation. Interval estimation including the estimation of means, differences of means, proportions, differences between proportions, variances and ratios of variances. Hypothesis testing including Neyman-Pearson lemma, power function and likelihood ratio test. Special tests involving means, variances and proportions. Nonparametric tests. Foundations of regression, correlation, design and analysis of experiments. Proofs of all main results. Practical examples illustrating the theory. The course can be used as a preparation for the statistical part of the fourth actuarial exam. Prerequisite: STAT 4351 or equivalent. (3-0) Y (2015-04-18 11:40:20)

STAT 4382 Stochastic Processes (3 semester credit hours) Stochastic models including Markov chains, random walks, Poisson processes, renewal processes, and an introduction to time series and forecasting. Prerequisite: STAT 4351 or equivalent. (3-0) Y (2015-04-18 11:40:20)

STAT 4V02 Independent Study in Statistics (1-6 semester credit hours) Independent study under a faculty member's direction. Student must obtain approval from participating mathematics faculty member and the undergraduate advisor. May satisfy the School of Natural Sciences and Mathematics' advanced writing requirement if it has a major writing/report component. May be repeated for credit as topics vary (9 semester credit hours maximum). Instructor consent required ([1-6]-0) S (2015-04-18 11:40:20)

STAT 4V97 Undergraduate Topics in Statistics (1-9 semester credit hours) May be repeated for credit as topics vary (9 semester credit hours maximum). Instructor consent required. ([1-9]-0) S (2015-04-18 11:40:20)

STAT 5191 Statistical Computing Packages (1 semester credit hour) Introduction to use of major statistical packages such as SAS, BMD, and Minitab. Based primarily on self-study materials. May not be used to fulfill degree requirements. Prerequisites: One semester of statistics and instructor consent required. (1-0) S (2015-04-18 11:40:21)

STAT 5351 Probability and Statistics I (3 semester credit hours) A mathematical treatment of probability theory. Random variables, distributions, conditioning, expectations, special distributions and the central limit theorem. The theory is illustrated by numerous examples. This is a basic course in probability and uses calculus extensively. Prerequisite: MATH 2451. (3-0) T (2015-04-18 11:40:21)

STAT 5352 Probability and Statistics II (3 semester credit hours) Theory and methods of statistical inference. Sampling, estimation, confidence intervals, hypothesis testing, analysis of variance, and regression with applications. Prerequisite: STAT 5351. (3-0) T (2015-04-18 11:40:21)

STAT 5390 Topics in Statistics - Level 5 (3 semester credit hours) May be repeated for credit as topics vary (9 semester credit hours maximum). Instructor consent required. (3-0) R (2015-04-18 11:40:21)

STAT 6313 (CS 6313) Statistical Methods for Data Science (3 semester credit hours) Statistical methods for data science. Statistical Methods are developed at an intermediate level. Sampling distributions. Point and interval estimation. Parametric and nonparametric hypothesis testing. Analysis of variance. Regression, model building and model diagnostics. Monte Carlo simulation and bootstrap. Introduction to a statistical software package. Prerequisite: CS 3341 or SE 3341 or STAT 3341 or equivalent. (3-0) S (2015-04-18 11:40:21)

STAT 6326 Sampling Theory (3 semester credit hours) Introduction to sampling theory and methods. Statistical inference for the popular sampling designs. Simple random sampling; stratified, systematic, cluster, unequal probability, multistage, and spatial sampling designs. Statistical methods for a finite population. Use of auxiliary data. Optimal allocation. Capture-recapture methods. Detectability. Multiplicity. Prerequisite: STAT 5351 and an undergraduate course in Statistics (STAT 2332 or STAT 3341 or STAT 3360 or equivalent). (3-0) T (2015-04-18 11:40:21)

STAT 6329 Applied Probability and Stochastic Processes (3 semester credit hours) Basic random processes used in stochastic modeling, including Poisson, Gaussian, and Markov processes with an introduction to renewal processes and queuing theory. Measure theory not required. Prerequisite: STAT 5351. (3-0) T (2015-04-18 11:40:21)

STAT 6331 Statistical Inference I (3 semester credit hours) Introduction to fundamental concepts and methods of statistical modeling and decision making. Basic distribution theory. Decision theory. Exponential families of models. Sufficiency. Estimation and hypothesis testing. Likelihood methods and optimality. Large sample approximations. Prerequisites: (STAT 5352 or equivalent) and (MATH 5302 or equivalent). (3-0) Y (2015-04-18 11:40:21)

STAT 6332 Statistical Inference II (3 semester credit hours) Elementary and advanced asymptotic methods, treating sample quantiles, U-statistics, differentiable statistical functions, and incluence curves, the MLE, L-statistics, M-statistics, and the bootstrap. Advanced aspects of statistical inference, likelihood-based inference, robust statistics. General forms of Neyman-Pearson Lemma. Metrics on spaces of probability distributions. Prerequisite: STAT 6331. Prerequisite or Corequisite: STAT 6344. (3-0) T (2015-04-18 11:40:21)

STAT 6337 Advanced Statistical Methods I (3 semester credit hours) Statistical methods most often used in the analysis of data. Univariate and multivariate statistics. P-values. Contingency tables. Simple and multiple regression. Model selection. Diagnostics and remedial measures. Analysis of residuals. Lack of fit. Ridge regression and multicollinearity. Influential data analysis. Categorical data and dummy variables. Nonlinear regression. Logistic regression. Data analysis using statistical software packages. Prerequisites: MATH 2418 and (STAT 5352 or STAT 6331). (3-0) T (2015-04-18 11:40:21)

STAT 6338 Advanced Statistical Methods II (3 semester credit hours) This course continues STAT 6337. Topics include one-way and multi-way analysis of variance, general and generalized linear models with fixed, random, and mixed effects, diagnostics, and implementation of statistical methods using statistical software. Prerequisite: STAT 6337. (3-0) T (2015-04-18 11:40:21)

STAT 6339 Linear Statistical Models (3 semester credit hours) Theoretical treatment of general and generalized linear models. Topics include random vectors; multivariate normal distribution; distributions of quadratic forms; general linear models for normal data; extension to generalized linear models for non-normal data such as binary, polytomous and count data; point and interval estimation; and hypothesis testing. Prerequisite: STAT 6331 or equivalent. (3-0) T (2015-04-18 11:40:21)

STAT 6341 Numerical Linear Algebra and Statistical Computing (3 semester credit hours) A study of computational methods used in statistics. Topics to be covered include the simulation of stochastic processes, numerical linear algebra, QR decomposition and least squares regression, SV decomposition and multivariate data, statistical programming languages, and graphical methods. Prerequisite: STAT 5352 or STAT 6337. (3-0) T (2015-04-18 11:40:21)

STAT 6343 Experimental Design (3 semester credit hours) Basic design principles; sample size computation; crossed and nested treatment factors; confounding; inference on contrasts; analysis of variance; analysis of covariance; designs such as completely randomized designs, factorial designs, complete block designs, incomplete block designs, Latin square designs, crossover designs, repeated measures designs and split plot designs; fractional replication in factorial experiments; variance components models; and implementation of statistical methods using a statistical software package. Prerequisite: STAT 6337 or equivalent. (3-0) T (2015-04-18 11:40:21)

STAT 6344 Probability Theory I (3 semester credit hours) Measure theoretic coverage of probability theory. Topics include: Axioms of probability, Integration; Distributions and moments; Probability Inequalities; Convergence of probability measures; Laws of large numbers; Central limit theorem; Three-series theorem; Zero-one laws; Glivenko-Cantelli theorem; Law of iterated logarithm; Conditional probability and expectation; Introduction to martingales. Prerequisite: MATH 5302 or equivalent. (3-0) T (2015-04-18 11:40:21)

STAT 6347 Applied Time Series Analysis (3 semester credit hours) Introduction to time series data; autocorrelation function; stationarity; classical decomposition of a time series; linear processes; forecasting stationary time series; basic time series models such as autoregressive models, moving average models, ARMA models, ARIMA models and seasonal ARIMA models; model fitting; model checking; model-based forecasting; regression with ARMA errors; spectral analysis; multivariate time series; and implementation of statistical methods using a statistical software package. Prerequisite: STAT 6337 or equivalent. (3-0) T (2015-04-18 11:40:21)

STAT 6348 Applied Multivariate Analysis (3 semester credit hours) Statistical methods used in analysis of multivariate data. Topics include Hotelling's T test, the multivariate ANOVA, principal components analysis, factor analysis, cluster analysis, discriminant analysis, classification problems, graphics and visualization tools. Emphasis on computations with R or other software. Additional topics may be covered as time allows. Prerequisite: STAT 5352 or STAT 6331. Corequisite: STAT 6337. (3-0) T (2015-04-18 11:40:21)

STAT 6365 Statistical Quality and Process Control (3 semester credit hours) Statistical methodology of monitoring, testing, and improving the quality of goods and services is developed at the intermediate level. Topics include control charts for variables and attributes, assessment of process stability and capability, construction and interpretation of CUSUM, moving average charts and V-masks, optimal sampling techniques, and evaluation of operating-characteristic curves and average time to detection. Prerequisite: STAT 5351 or equivalent. (3-0) T (2015-04-18 11:40:21)

STAT 6390 Topics in Statistics - Level 6 (3 semester credit hours) Topics selected from but not limited to choices such as spatial statics, nonparametric curve estimation, functional data analysis, statistical learning and data mining, actuarial science, sampling theory, statistical quality and process control, sequential analysis, survival analysis, longitudinal data analysis, categorical data analysis, and clinical trials, for example. May be repeated for credit as topics vary (9 semester credit hours maximum). (3-0) R (2015-04-18 11:40:21)

STAT 6V98 Masters Thesis (3-9 semester credit hours) Pass/Fail only. May be repeated for credit. Instructor consent required. ([3-9]-0) S (2015-04-18 11:40:21)

STAT 6V99 Statistical Consulting (1-3 semester credit hours) Practical experience in collaboration with individuals who are working on problems which are amenable to statistical analysis. Problem formulation, statistical abstraction of the problem, and analysis of the data. May be repeated for credit. Only a maximum of three semester credit hours may be used to fulfill the master's degree. Instructor consent required. ([1-3]-0) T (2015-04-18 11:40:21)

STAT 7330 Decision Theory and Bayesian Inference (3 semester credit hours) Statistical decision theory and Bayesian inference are developed at an intermediate mathematical level. Topics include utility theory; Bayesian estimation, hypothesis testing, and prediction; empirical and hierarchical Bayes rules; Bayesian robustness; admissibility; minimax decisions and introduction to game theory. Prerequisite: STAT 6331. (3-0) T (2015-04-18 11:40:21)

STAT 7331 Multivariate Analysis (3 semester credit hours) Vector space foundations and geometric considerations. The multivariate normal distribution: properties, estimation, and hypothesis testing. Hotelling's T statistic. Classification problems. Sample covariance matrix and the Wishart distribution. General linear hypothesis and MANOVA. Testing independence of sets of variables. Principal components, canonical correlations, factor analysis. Curse of dimensionality. Dimension Reduction. Multidimensional Classification and Clustering. Multivariate symmetry. Multivariate signs, ranks, and quantiles. Functional data analysis. Selected further topics. Prerequisite: STAT 6331 or equivalent. (3-0) T (2015-04-18 11:40:21)

STAT 7334 Nonparametric and Robust Statistical Methods (3 semester credit hours) Order statistics, ranks, and related distribution theory. Sign, signed rank, and permutation statistics. U-statistics, L-statistics, M-statistics, R-statistics. One- and multi-sample location and scale problems. Nonparametric ANOVA. Pitman asymptotic relative efficiency. Locally most powerful rank tests. Maximum likelihood estimation for nonparametric families. Minimax asymptotic variance and minimum bias criteria for robust estimation. Robust confidence limits. Optimal influence curves. Nonparametric/robust density estimation, regression curve estimation, and smoothing. Nonparametric and robust methods for multivariate data. Selected other topics. Prerequisite: STAT 6331 or equivalent. (3-0) T (2015-04-18 11:40:21)

STAT 7338 Time Series Modeling and Filtering (3 semester credit hours) Theory of correlated observations observed sequentially in time. Stationary processes, Autocovariance function. ARMA models. Optimal forecasting in time domain and in frequency domain. Spectral representation. Estimation and model selection. Nonstationary time series models. Prerequisite: STAT 6331. (3-0) T (2015-04-18 11:40:21)

STAT 7345 Advanced Probability and Stochastic Processes (3 semester credit hours) Taught as a continuation of STAT 6344. Exponential probability inequalities. Large deviation theory. Martingales, sub- and supermartingales, random walk, Markov chains, Yule and Poisson processes, the general birth and death process, shot noise, branching processes, renewal processes, Brownian motion and diffusion, stationary processes, and the empirical process. Selected other topics. Prerequisite: STAT 6344. (3-0) T (2015-04-18 11:40:21)

STAT 7390 Topics in Statistics - Level 7 (3 semester credit hours) Topics selected from but not limited to choices such as spatial statistics, nonparametric curve estimation, functional data analysis, statistical learning and data mining, actuarial science, sampling theory, statistical quality and process control, sequential analysis, survival analysis, longitudinal data analysis, categorical data analysis, and clinical trials, for example. May be repeated for credit as topics vary (9 semester credit hours maximum). Instructor consent required. (3-0) R (2015-04-18 11:40:21)

STAT 8V02 Individual Instruction in Statistics (1-6 semester credit hours) Pass/Fail only. May be repeated for credit. Instructor consent required. ([1-6]-0) S (2015-04-18 11:40:21)

STAT 8V03 Advanced Topics in Statistics (1-6 semester credit hours) Pass/Fail only. May be repeated for credit. Instructor consent required. ([1-6]-0) R (2015-04-18 11:40:21)

STAT 8V07 Research in Statistics (1-9 semester credit hours) Open to students with advanced standing, subject to approval of the graduate advisor. Pass/Fail only. May be repeated for credit. Instructor consent required. ([1-9]-0) S (2015-04-18 11:40:21)

STAT 8V99 Dissertation (1-9 semester credit hours) Pass/Fail only. May be repeated for credit. Instructor consent required. ([1-9]-0) S (2015-04-18 11:40:21)