# Graduate Courses in Probability & Statistics

#### 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. *Eden.* 4 cr, 1st sem.

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

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

#### CAS MA 575 Linear Models

Prereq: CAS MA 214, 242 and 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. 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.

#### CAS MA 578 Bayesian Statistics

Prereq: CAS MA 581 and MA 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 MA 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. *Taqqu. *4 cr, 1st sem.

#### CAS MA 582 Mathematical Statistics

Prereq: CAS MA 381 or MA 581. Point estimation including unbiasedness, efficiency, consistency, sufficiency, minimum variance unbiased estimator, Rao-Blackwell theorem, and Rao-Cramer inequality. Also includes 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. *Ginovyan.* 4 cr, 2nd sem.

#### CAS MA 583 Introduction to Stochastic Processes

Prereq: CAS MA 381 or MA 581 or consent of instructor. Basic concepts and techniques of stochastic processes 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. *Eden.* 4 cr, 2nd sem.

#### CAS MA 584 Multivariate Statistical Analysis

Prereq: CAS MA 213 ; CAS MA 242 ; 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

#### 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. *Gangopadhyay* 4 cr, 2nd sem.

#### CAS MA 588 Nonparametric Statistics

Prereq: CAS MA 582; or equivalent, 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.

#### CAS MA 589: Computational Statistics

Prereq: CAS MA 213; AND CAS MA 242 (OR CAS MA 442), AND CAS MA 581; or equivalent with consent of instructor. Topics from computational statistics that are relevant to modern statistical applications: random number generation, sampling, Monte Carlo methods, computational inference, MCMC methods, graphical models, data partitioning, and bootstrapping. Emphasis on developing solid conceptual understanding of the methods through applications.

#### GRS MA 614 Statistical Methods 2

For graduate students in education and the social sciences. Not open to CAS students. Students may receive credit for no more than one of the following courses: CAS MA 116, MA 214, and 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. *Heeren. *4 cr, 1st sem.

#### GRS MA 681: Accelerated Introduction to Statistical Methods for Quantitative Research

Prereqs: CAS MA 225 and CAS MA 242; or their equivalents. Introduction to statistical methods relevant to research in the computational sciences. Core topics include probability theory, estimation theory, hypothesis testing, linear models, GLMs, and experimental design. Emphasis on developing a firm conceptual understanding of the statistical paradigm through data analyses.

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

Prereq: one year of statistics. Application of multivariable data analytic techniques. Multiple linear 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. *Heeren.* 4 cr, 2nd sem.

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

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

#### GRS MA 750 Advanced Statistical Methods I

Prereq: CAS MA 575 and CAS MA 581, or consent of instructor. First in a two-semester PhD sequence on post-classical statistical methods and their applications. Selection from topics in non- and semi-parametric modeling and inference, such as smoothing, splines, generalized additive models, projection pursuit, and classification and regression trees. *Gangopadhyay. *4 cr, 1st sem.

#### GRS MA 751 Advanced Statistical Methods II

Prereq: CAS MA 575 and CAS MA 581, or consent of instructor. Second in a two-semester PhD sequence on post-classical statistical methods and their applications. Selection from topics in statistical learning, such as regularized basis methods, kernel methods, boosting, neural networks, support vector machines, and graphical models. *Kolaczyk.* 4 cr, 2nd sem.

#### GRS MA 770 Mathematical and Statistical Methods of Bioinformatics

Prereq: graduate standing or advanced undergraduate math/statistics major, (CASMA225), (CASMA242), and previous work in mathematical analysis and probability.

Mathematical and statistical bases of bioinformatics methods and their applications. Hidden Markov models, kernel methods, mathematics of machine learning approaches, probabilistic sequence alignment, Markov chain Monte Carlo and Gibbs sampling, mathematics of phylogenetic trees, and statistical methods in microarray analysis.

#### GRS MA 779 Probability Theory I

Prereq: CAS MA 511 or consent of instructor. Introduction to probability with measure theoretic foundations. Fundamentals of measure theory. Probability space. Measurable functions and random variables. Expectation and conditional expectation. Zero-one laws and Borel-Cantelli lemmas. Characteristic functions. Modes of convergence. Uniform integrability. Skorokhod representation theorem. Basic limit theorems. *Taqqu.* 4 cr,1st sem.

#### GRS MA 780 Probability Theory II

Prereq: GRS MA 779 or consent of instructor. Probability topics important in applications and research. Laws of large numbers. Three series theorem. Central limit theorems for independent and non-identically distributed random variables. Speed of convergence. Large deviations. Laws of the iterated logarithm. Stable and infinitely divisible distributions. Discrete time martingales and applications. *Taqqu. *4 cr, 2nd sem.

#### GRS MA 781 Estimation Theory

Prereq: CAS MA 581, MA 582, or consent of instructor. Review of probability, populations, samples, sampling distributions, and delta theorems. Parametic point estimation. Rao-Cramer inequality, sufficient statistics, Rao-Blackwell theorem, maximum likelihood estimation, least squares estimation, and general linear model of full rank. Confidence intervals. Bayesian analysis and decision theory. *Ginovyan.* 4 cr, 1st sem.

#### GRS MA 782 Hypothesis Testing

Prereq: GRS MA 781 or consent of instructor. Parametric hypothesis testing, uniformly and locally the most powerful tests, similar tests, invariant tests, likelihood ratio tests, linear model testing, asymptotic theory of likelihood ratio, and chi-squared test. Logit and log-lin analysis of contingency tables. 4 cr, 2nd sem.

#### GRS MA 791 Recent Advances in Probability and Statistics I

Prereq: consent of instructor. Participants discuss ongoing research, as well as important results that have recently appeared in the literature.

#### GRS MA 792 Recent Advances in Probability and Statistics II

Prereq: consent of instructor. Participants discuss ongoing research, as well as important results that have recently appeared in the literature.

#### GRS MA 881, 882 Seminar: Statistics

Prereq: GRS MA 782. Real problems in experimental design and data analysis presented by clients from various other departments. The art of statistical consulting in a variety of applied areas.

#### GRS MA 883, 884 Seminar: Probability and Statistics

Prereq: consent of instructor. Invited speakers from the United States and abroad describe open problems and recent results.

### Directed Study and Research

#### GRS MA 991, 992 Directed Study: Statistical Inference and Probability

Variable cr.

### Related Courses in Other Departments

Additional courses of related interest at Boston University include courses in biostatistics and statistical genetics through the Department of Biostatistics, courses in bioinformatics through the Bioinformatics Program, courses in data mining and machine learning through the Department of Computer Science, and courses in artificial neural network modeling through the Department of Cognitive and Neural Systems.