The University of Arizona 199395 General Catalog Catalog Home All UA Catalogs UA Home

Statistics (STAT) Economics Building, Room 200 (520) 6214158 Professors Yashaswini Mittal, Head, Dan Bailey (Emeritus), J.L. Denny, Jean E. Weber Associate Professors Scott Emerson, A. Larry Wright Assistant Professors Chengda Yang Study of statistics enables one to model the uncertainty in data and draw organized scientific conclusions from it. Data from different disciplines post different statistical problems and hence statistics is inherently an interdisciplinary field. The department offers both theoretical and applied courses. Statistics is available as a major in the Master of Science and the Doctor of Philosophy degrees. 160. Introduction to Statistics (3) I II Descriptive statistics. Basic probability concepts and probability distributions, elementary sampling theory and techniques of estimation, hypothesis testing, regression and correlation. Some analysis of variance and nonparametric tests if time permits. Not applicable to the math major. P, MATH 117R/S. 163. Beginning Statistics in Bioscience (3) I II Basic concepts of probability and statistics. Descriptive statistics commonly used in biological and medical sciences such as mean, standard deviation, odds ratio and risk. Interpretation of statistical plots and charts. Basic idea of estimation, regression and hypothesis testing. Emphasis on statistical concepts and interpretations of tests. P, MATH 117R/S. 263. Statistical Methods in Biological Sciences (3) I II Organization and summarization of data, concepts of probability, probability distributions of discrete and continuous random variables, point and interval estimation, elements of hypothesis testing, regression and correlation analysis, chisquare distribution and analysis of frequencies, introduction to analysis of variance as well as nonparametric statistics, with special emphasis on analysis of biological and clinical data. P, MATH 119, 123. 275. Statistical Methods in Management (3) I II Statistical analysis and methods with a view toward applications in business and economics. Basic concepts of probability, random variables, probability distributions and sampling distributions. Statistical inference techniques such as estimation, hypothesis, testing, regression, correlation and analysis of variance are explored through examples and via the use of Minitab. Emphasis is put on the interpretations of Minitab outputs rather than running the Minitab itself. P, MATH 119, 123. 361. Statistics for Engineering and the Physical Sciences (3) I II Probability theory, point and interval estimation, hypothesis testing and regression analysis; applications to quality control and reliability theory. P, 9 units of calculus. 451. Introduction to Statistical Methods (3) I II Sample spaces, random variables, probability. Distribution: binomial, normal, Poisson, geometric. Expectations, variance, moment generating functions. Central limit theorem and laws of large numbers. Basic concepts of sampling distributions. Estimation, hypothesis testing. An introductory theoretical course emphasizing concepts, and interpretations. Limited mathematical proofs. P, MATH 123 or MATH 125b, and one of STAT 160, STAT 263, STAT 275, STAT 361. 464. Theory of Probability (3) I II (Identical with MATH 464) May be convened with 564. 466a. Theory of Statistics (3) I Sampling theory, point estimation, limiting distributions, testing hypotheses, confidence intervals, large sample methods, elements of multivariate analysis. P, 464. (Identical with MATH 466a) May be convened with 566a. 468. Applied Stochastic Processes (3) II (Identical with MATH 468) May be convened with 568. 509. Statistics for Research (4) I II Statistical concepts and methods applied to research in other scientific disciplines. Principles of estimation and hypothesis testing for standard one and twosample procedures. Correlation, linear regression,. Contingency tables and analysis of variance. Not open to majors. P, college algebra (Identical with GENE 509 and TOX 509) 548. Introduction to Statistical Packages (3) I Basic structure of general purpose statistical software. Data formats, storage and transmission. Relation between hardware and software. Usage of major statistical packages SAS, BMDP, and SPSS on both personal and mainframe computers. Open to graduate students in all disciplines. 551. Applied Statistics I: Regression Analysis (3) I Regression analysis including simple linear regression, and multiple linear regression. Regression, diagnostics, variable selection techniques, collinearity, nonlinear models and transformations, case studies. P, 451 and 509, MATH 223. 552. Applied Statistics II: Experiment Design (3) II Principles of designing experiments. Randomization, blocked designs, factorial experiments, response surface designs, repeated measures, analysis of contrasts, multiple comparisons, multiple comparisons, and variance component analysis. P, 451/551 and 509, MATH 223. 553. Applied Multivariate Analysis (3) II Methods for analysis of multivariate observations. Random vectors, multivariate expectations and covariance matrices. Multivariate normal distribution. Hotelling's Tsquare distribution. Multivariate analysis of variance and linear regression. Principal component and discriminant analysis, classification, clustering, canonical correlation and factor analysis. P, 451 and 509. 554. Applied Time Series Analysis (3) I Methods for analysis of time series data. Time domain techniques; ARIMA models, estimation of process mean and autocovariance, model fitting, forecasting methods. missing data. P, 451 and 509. 560a560b. Probability and Random Processes (33) I First part of the sequence will deal with probability. Sample spaces, basic axioms of probability, combinatorial methods, conditional probability and distributions, independence. Random variables, discrete and continuous distributions. Binomial, Poisson, geometric, normal, exponential and gamma distributions. Transformations of random variables and Jacobians, expectation, variance and other moments, laws of large numbers, central limit theorem. Characteristic and generating functions. Fundamental probability concepts without the use of measure theory. P, two years of calculus., e.g. MATH 125a125b and MATH 223. 560b: II Second part of the sequence will cover elementary random processes. Markov and stationary processes, random walk, renewal theory, queuing networks, branching processes, Poisson processes, martingales. Theory as well as some applications. No measure theory requirement. P, 560a. 562. Sampling Survey Theory and Methods (3) II Introduction to planning, execution, and analysis of surveys, methods of sampling, estimation of population values, estimation of sampling error and efficiency of methods. Special emphasis on finite population applications. P, 509. 563. Nonparametric Statistics (3) I Distribution free statistical methods for nominal and ordinal data. Measures of association. Goodness of fit and runs tests. Analysis of one or more groups. Correlation and regression of ranked data. P, 509. 564. Theory of Probability (3) I II (Identical with MATH 564) May be convened with 464. 566a566b. Theory of Statistics (33) 566a: I For a description of course topics, see 466a. Graduatelevel requirements include more extensive problem sets or advanced projects. P, 464. (Identical with MATH 566a) May be convened with 466a. 566b: II Hypothesis testing. Type I and type II errors, NeymanPearson theory, uniformly most powerful unbiased and invariant tests. Likelihood ratio tests. Confidence intervals. Sequential analysis, nonparametric and robust methods. Theoretical foundation of statistical inference. P, 566a. 568. Applied Stochastic Processes (3) II (Identical with MATH 568) May be convened with 468. 572. Categorical Data Analysis (3) II Twoway contingency tables, logistic, probit, loglog regression. Loglinear models. Model selection techniques. Testing goodness of fit models. Numerical methods for finding MLE. Treatment of ordinal and nominal variables. Poisson and multinomial samplings. P, 451 and 509. 595. Colloquium a. Statistics (1) [Rpt./3 units] I II Open to majors only 596. Seminar a. Research Methods (14) [Rpt./6 units] I II 597. Workshop a. Data Analysis (1) [Rpt./3 units] I II Open to majors only or with permission of instructor. P, 451, 509 or equivalent. 641. Statistical Consulting (3) I II A course for statistics graduate students providing experience in statistical consulting. Client and statistician relationships, communication skills, computing and graphical analysis resources, approaches to problems with measurement error and missing data. Consulting practice with client research problems under faculty supervision. 1R, 6L. P, advanced standing in the masters program. 660. Linear Models (3) I Multivariate normal distribution, distribution of quadratic forms. Generalized inverses. Theory of estimation and hypothesis tests for full rank linear models and less than full rank models applied to regression models. Analysis of variance models, variance component and mixed models and unbalanced data models. Theoretical foundation course for linear model analysis techniques. P, 566a, linear algebra, e.g. MATH 413. 661. Probability Foundations of Mathematical Statistics (3) I 199495 Measure theorybased probability theory needed for mathematical statistics. Measurable space, Lebsgue measure and integral, distribution functions, random variables, expectation and conditional expectation, characteristic functions, law of large number, central limit theory, modes of convergence, complete and sufficient statistics, martingale. P, 560a, MATH 523a, or consent of instructor. 667. Theory of Estimation (3) I Measure theory based point estimation theory. Unbiasedness, information inequality. Equivariance, locationscale family, exponential families. Maximum likelihood, Bayes and minimax estimation. Admissibility of estimators. Convergence properties. Asymptotic optimality. P, 566b, MATH 523. (Identical with MATH 667) 668. Theory of Testing of Hypotheses (3) II Measuretheorybased hypothesistesting theory. Simple and composite null and alternative hypotheses. Test function. Hypothesis testing in exponential families, testimability, i.e. uniformly most powerful, unbiased, alphasimilar, minimax and invariant tests. Likelihood ratio tests. Admissibility. Testing population means. Nonparametric tests. P, 566b, MATH 523. (Identical with MATH 668) 
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