# Undergraduate Courses in Probability & Statistics

#### CAS MA 113 Elementary Statistics

CAS MA 113 may not be taken for credit by any student who has completed any MA course numbered 300 or higher. Students may receive credit for not more than one of the following courses: CAS MA 113, MA 115, or MA 213. Basic concepts of estimation and tests of hypotheses, ideas from probability; one-, two-, and multiple-sample problems. Applications in social sciences. Primarily for students in the social sciences who require a one-semester introduction to statistics; others should consider CAS MA 115 or MA 213. 4 cr, either sem. (MCS)

#### CAS MA 115 Statistics I

CAS MA 115 may not be taken for credit by any student who has completed any MA course numbered 300 or higher. Students may receive credit for not more than one of the following courses: CAS MA 113, MA 115, or MA 213. Numerical and graphical summaries of univariate and bivariate data. Basic probability, random variables, binomial distribution, normal distribution. One-sample statistical inference for normal means and binomial probabilities. Primarily for students in the social sciences with limited mathematics preparation. 4 cr, either sem. (MCS)

#### CAS MA 116 Statistics II

CAS MA 116 may not be taken for credit by any student who has completed any MA course numbered 300 or higher. Prereq: CAS MA 115 or equivalent. Students may receive credit for not more than one of the following courses: CAS MA 116, MA 214, or MA 614. One- or two-sample inference for normal means and binomial probabilities, analysis of variance, simple linear regression, multiple regression, analysis of categorical data. Introduction to survey design and design of experiments. Primarily for students in the social sciences with limited mathematics preparation. 4 cr, either sem. (MCS)

#### CAS MA 213 Basic Statistics and Probability

Prereq: good background in high school algebra. Students may receive credit for not more than one of the following courses: CAS MA 113, MA 115, or MA 213. Elementary treatment of probability densities, means, variances, correlation, independence, the binomial distribution, the central limit theorem. Stresses understanding and theoretical manipulation of statistical concepts. 4 cr, either sem. (MCS)

#### CAS MA 214 Applied Statistics

Prereq: CAS MA 213 or consent of instructor. Students may receive credit for not more than one of the following courses: CAS MA 116, MA 214, or MA 614. Inference about proportions, goodness of fit, student’s t-distribution, tests for normality; two-sample comparisons, regression and correlation, tests for linearity and outliers, residual analysis, contingency tables, analysis of variance. 4 cr, either sem. (MCS)

#### CAS MA 416 Analysis of Variance

Prereq: CAS MA 116 or 214 or equivalent. Fundamental concepts and analytical skills in analysis of variance, including crossed and nested designs, as well as fixed- and random-effect models. Trend analysis for repeated measures, expected mean squares, and nonparametric techniques. SAS is used throughout the course. 4 cr, 1st sem.

#### CAS MA 421 Modern Statistical Modeling and Data Analysis with Splus

Prereq: CAS MA 115 or 213 and MA 116 or 214. Provides a non-technical descriptive introduction to modern techniques in data modeling via software Splus. Topics include linear and nonlinear, nonparametric and semiparametric regression, Bayesian models and computations, introduction to data mining, association rules, decision trees, and neural network algorithms. 4 cr, Summer I.

#### CAS MA 568 Statistical Analysis of Point Process Data

Prereq: CAS MA 213 and CAS MA 214 or consent of instructor. Introduces the theory of point processes and develops practical problem-solving skills to construct models, assess goodness-of-fit, and perform estimation from point process data. Applications to neural data, earthquake analysis, financial modeling, and queuing theory. 4 cr, 1st sem.

#### CAS MA 570 Stochastic Methods of Operations Research

Prereq: CAS MA 225 or 230 and MA 242 or 442. Poisson processes, Markov chains, queuing theory. Matrix differential equations, differential-difference equations, probability- and moment-generating functions, single- and multiple-channel queues, steady-state and transient distributions. 4 cr, 2nd sem.

#### CAS MA 572 Introduction to Mathematical Finance

Prereq: CAS MA 226 or 231 and MA 381 or 581. A rigorous mathematical introduction to developments in the field of finance. Mathematics of modern portfolio theory, capital asset pricing model, and arbitrage pricing theory. Derivation of pricing models for options, futures, and swaps based on concepts from Itô calculus. 4 cr, either sem.

#### CAS MA 575 Linear Models

Prereq: CAS MA 214 and CAS MA 242 and CAS MA 581 or consent of instructor. Post-introductory course in linear models, with focus on both principles and practice. Simple and multiple linear regression, weighted and generalized least squares, polynomials and factors, transformations, regression diagnostics, variable selection, and a selection from topics on extensions of linear models. 4 cr, 1st sem.

#### CAS MA 576 Generalized Linear Models

Prereq: CAS MA 575 or consent of instructor. Covers topics in linear models beyond MA 575: generalized linear models, analysis of binary and polytomous data, log-linear models, multivariate response models, non-linear models, graphical models, and relevant model selection techniques. Additional topics in modern regression as time allows. 4 cr, 2nd sem.

#### CAS MA 577 Mathematics of Financial Derivatives

Prereq: CAS MA 581 or consent of instructor. Develops the probabilistic tools used in finance and presents the methodologies that are used in the pricing of financial derivatives. No previous knowledge of finance is required. 4 cr, either sem.

#### CAS MA 578 Bayesian Statistics

Prereq: CAS MA 581 and 582. The principles and methods of Bayesian statistics. Subjective probability, Bayes rule, posterior distributions, predictive distributions. Computationally based inference using Monte Carlo integration and Markov chain simulation. Hierarchical models, mixture models, model checking, and methods for Bayesian model selection. 4 cr, 2nd sem.

#### CAS MA 581 Probability

Prereq: CAS MA 225 or 230 or consent of instructor. Basic probability, conditional probability, independence. Discrete and continuous random variables, mean and variance, functions of random variables, moment generating function. Jointly distributed random variables, conditional distributions, independent random variables. Methods of transformations, law of large numbers, central limit theorem. (Cannot be taken for credit in addition to CAS MA 381 or MA 590.) 4 cr, 1st sem.

#### CAS MA 582 Mathematical Statistics

Prereq: CAS MA 381 or 581. Point estimation including unbiasedness, efficiency, consistency, sufficiency, minimum variance unbiased estimator, Rao-Blackwell theorem, and Rao-Cramer inequality. Maximum likelihood and method of moment estimations; interval estimation; tests of hypothesis, uniformly most powerful tests, uniformly most powerful unbiased tests, likelihood ratio test, and chi-square test. 4 cr, 2nd sem.

#### CAS MA 583 Introduction to Stochastic Processes

Prereq: CAS MA 381 or 581 or consent of instructor. Basic concepts and techniques of stochastic process as they are most often used to construct models for a variety of problems of practical interest. Topics include Markov chains, Poisson process, birth and death processes, queuing theory, renewal processes, and reliability. 4 cr, 2nd sem.

#### CAS MA 584 Multivariate Statistical Analysis

Prereq: CAS MA 213 and CAS MA 242 and CAS MA 581 or consent of instructor. Presents statistical concepts and methods, and their application for the exploration, regression, testing, visualization, and clustering of multivariate data. Both classical and modern techniques are developed, including methods for analysis of high dimensional and non-euclidean data. 4 cr, 2nd sem.

#### CAS MA 585 Time Series and Forecasting

Prereq: CAS MA 581 or consent of instructor. Autocorrelation and partial autocorrelation functions; stationary and nonstationary processes; ARIMA and Seasonal ARIMA model identification, estimation, diagnostics, and forecasting. Modeling financial data via ARCH and GARCH models. Volatility estimation; additional topics, including long-range dependence and state-space models. 4 cr, either sem.

#### CAS MA 586 The Design of Experiments

Prereq: CAS MA 582 or equivalent or consent of instructor. Randomized blocks, Latin and Graeco-Latin squares, factorial arrangements with confounding and fractional replication, split-plot, crossover, and response surface designs. Treatment of missing data, group sizes, relative efficiency, relationship between design and analysis. 4 cr, 2nd sem.

#### CAS MA 587 Sampling Design: Theory and Methods

Prereq: CAS MA 582 or equivalent or consent of instructor. Stratified, cluster, systematic, multistage, double, and inverse sampling; optimum sample size, relative efficiency, sampling with unequal probabilities, types of estimators (ratio and regression) and their properties. Measurement error nonresponse and randomized response models. 4 cr, 1st sem.

#### CAS MA 588 Nonparametric Statistics

Prereq: CAS MA 582 or equivalent, or consent of instructor. The theory and logic in the development of nonparametric techniques including order statistics, tests based on runs, goodness of fit, rank-order (for location and scale), measures of association, analysis of variance, asymptotic relative efficiency. 4 cr, 2nd sem.

#### GRS MA 614 Statistical Methods

For graduate students in education and the social sciences. Not open to CAS students. Students may receive credit for not more than one of the following courses: CAS MA 116, MA 214, or MA 614. Second course in statistics, embodying basic statistical methods used in educational and social science research. Reviews all basic concepts covered in a first statistics course and presents, in detail, more advanced topics such as analysis of variance, covariance, experimental design, correlation, regression, and selected nonparametric techniques. A problem-solving course; students carry out analysis of data taken from educational and other social science sources. 4 cr, 1st sem.

#### GRS MA 684 Applied Multiple Regression and Multivariable Methods

Prereq: one year of statistics. Application of multivariate data analytic techniques. Multiple regression and correlation, confounding and interaction, variable selection, categorical predictors and outcomes, logistic regression, factor analysis, MANOVA, discriminant analysis, regression with longitudinal data, repeated measures, ANOVA. 4 cr, 2nd sem.

#### GRS MA 685 Advanced Topics in Applied Statistical Analysis

Prereq: GRS MA 684 or consent of instructor. Continues topics of CAS MA 684 at a more advanced level. Canonical correlation, multivariate analysis of variance, multivariate regressions. Categorical dependent variables techniques; discriminant analysis, logistic regression, log-linear analysis. Factor analysis; principal-axes, rotations, factor scores. Cluster analysis. Power analysis. Extensive use of statistical software. 4 cr, 1st sem.