Education / Graduate Education / PhD Programs / Statistics / About the Program / Curriculum Curriculum Graduate Course Schedules Spring 2016 Fall 2015 Spring 2015 Fall 2014 Graduate Course Descriptions BST 401 Probability Theory BST 402 Stochastic Processes BST 411 Statistical Inference BST 412 Large-Sample Theory and Methods BST 413 Bayesian Inference BST 416 Applied Statistics BST 421 Sampling Techniques BST 422 Design of Experiments BST 426 Linear Models BST 431 Introduction to Computational Biology BST 432 Introduction to Bioinformatics BST 433 Introduction to Computational Systems Biology BST 435 Bioinformatics Databases and Applications BST 441 Applied Multivariate Analysis BST 450 Data Analysis BST 451 Exploratory Data Analysis BST 452 Design of Experiments BST 463 Introduction to Biostatistics BST 464 Applied Linear Regression BST 465 Design of Clinical Trials BST 466 Categorical Data Analysis BST 467 Applied Statistics in the Biomedical Sciences BST 476 Introduction to Linear Models BST 477 Introduction to Statistical Software I BST 478 Introduction to Statistical Software II BST 479 Generalized Linear Models BST 487 Seminar in Statistical Literature BST 491 Reading Course at the Master's Level BST 493 Internship/Applied Project BST 495 Research at the Master's Level BST 496 Wet/Dry Lab Rotation BST 511 Topics in Statistical Inference I BST 512 Topics in Statistical Inference II BST 513 Analysis of Longitudinal and Dependent Data BST 514 Survival Analysis BST 520 Current Topics in Bioinformatics BST 521 Advanced Computing for Bioinformatics and Computational Biology BST 522 Big Data in Biomedical Research BST 523 Dynamic Modeling for Biological Processes BST 525 Introduction to Health Informatics BST 526 High-Dimensional Bioinformatics Data Analysis and Inference BST 527 Networks and Graphical Models in Genomic Applications BST 531 Nonparametric Inference BST 536 Sequential Analysis BST 541 Multivariate Analysis BST 550 Topics in Data Analysis BST 570 Topics in Biostatistics BST 582 Introduction to Statistical Consulting BST 590 Supervised Teaching BST 591 Reading Course at the PhD Level BST 592 Supervised Statistical Consulting BST 595 Research at the PhD Level Full Descriptions BST 401 Probability Theory Prerequisites: MTH 265 or equivalent (or permission) Description: Probability spaces; random variables; independence; distributions; expectation; characteristic functions and inversion theorems; convergence; laws of large numbers; central limit theorem. Offered: Fall BST 402 Stochastic Processes Prerequisites: BST 401 Description: Markov chains; birth-death processes; random walks; renewal theory; Poisson processes; Brownian motion; branching processes; martingales; with applications. Offered: Fall BST 411 Statistical Inference Prerequisites: STT 203 or equivalent Description: Probability distributions, transformations and sampling distributions; statistical models; estimation, hypothesis testing, and confidence intervals for parametric models; introduction to large-sample methods. Offered: Fall BST 412 Large-Sample Theory and Methods Prerequisites: BST 401 and BST 411 Description: Weak convergence; asymptotic linearity; local analysis; large sample estimation, maximum likelihood estimation and M-estimation; Wald, likelihood ratio, and score tests; confidence regions; nuisance parameters; efficiency; multinomial chi-square tests. Offered: Spring BST 413 Bayesian Inference Prerequisites: BST 411 Description: Posterior distributions for single and multiple parameter models under conjugacy; hierarchical models; noninformative and informative prior distributions; modern computational techniques, including Markov chain Monte Carlo; model checking; posterior predictive checks; sensitivity analysis. Offered: Fall BST 416 Applied Statistics Prerequisites: STT 211 or STT 212 or BST 463 or equivalent Description: One- and two-way analysis of variance; simple and multiple regression; analysis of covariance; analysis of residuals, use of transformations; topics from contingency table analysis and nonparametric statistics. Emphasis on real examples from the biomedical and social sciences, with extensive use of statistical software. Offered: Spring BST 421 Sampling Techniques Prerequisites: STT 211, STT 212 or STT 213, and 203 or equivalent Description: Simple random, stratified, systematic, and cluster sampling; estimation of the means, proportions, variance, and ratios of a finite population. Ratio and regression methods of estimation and the use of auxiliary information. The nonresponse problem. Offered: Fall BST 422 Design of Experiments Prerequisites: BST 416 or BST 464 or BST 476 Description: Basic designs and their principles; randomization; blocking; use of concomitant information. Offered: Spring BST 426 Linear Models Prerequisites: STT 203 and MTH 235 Description: Theory of least-squares; point estimation in the general linear model; projection operators, estimable functions and generalized inverses; tests of general linear hypotheses; power; confidence intervals and ellipsoids; simultaneous inference; linear and polynomial regression; analysis of variance and analysis of covariance models; fixed, random, and mixed effects; correlation; prediction. Offered: Spring BST 431 Introduction to Computational Biology Prerequisites: Calculus, Differential Equations and BST401 Description: Topics include: Basics of statistical learning; Nucleic acid sequence modeling; Protein sequence modeling; Molecule structure and visualization; Data exploration by clustering; Phylogenetic trees; Cell pathway; Network dynamics and topology analysis; Modeling molecular events; Biochemical and cell kinetics; Compartmental analysis; Population dynamics; Basics of digital image processing; Image feature extraction and pattern analysis; and Image modeling. BST 432 Introduction to Bioinformatics Prerequisites: BST 401 and BST 411 Description: The course will emphasize the application of statistical theory to the analysis of high throughput data, and include the following topics: 1) Introduction to Bioconductor (gene expression structure, annotation and metadata, creating packages). 2) Molecular profiles (mRNA, cDNA, microRNA, proteomics). 3) Platforms (Affymetrix and other microarrays, PCR, RNA seq). 4) Quality control (quality assessment, batch-effects). 5) Exploratory methods (graphical methods, clustering, principal component analysis and other dimension reduction techniques). 6) Differential expression and multiple hypothesis testing. 7) Gene set analysis, ontologies, enrichment analysis. 8) Classification (feature selection, multivariate methods, machine learning, cross-validation). 9) Pathway and network models (relevance networks, probabilistic graphical models, Bayesian networks, Markov networks, Boolean networks). BST 433 Introduction to Computational Systems Biology Prerequisites: Calculus, Differential Equations, BST 401 and BST 411 Description: This course intends to introduce students with basic concepts of a “system” and system theory with applications to modeling biological systems and processes. In particular, we train students to have a systems thinking in biomedical research with a solid systems science approach. The contents include 1) Introduction to systems concepts and systems theory. 2) Mathematical representations of systems. 3) Linear ODE systems. 4) Nonlinear ODE systems. 5) Network motifs. 6) Network robustness. 7) Modeling of biochemical systems. 8) Gene regulatory network systems. 9) Multi-scale biological systems. 10) Systems biology experimental design. 11) Identification of biological systems using experimental data. BST 435 Bioinformatics Databases and Applications Description: The contents include: 1) Introduction to biological databases 2) Sequence databases 3) Structure databases 4) Interaction databases 5) Pathway databases 6) Heterogeneity in databases 7) Data complexity of biological data 8) Database design 9) Database integration and information retrieval. BST 441 Applied Multivariate Analysis Prerequisites: BST 476 or BST 426 Description: Methodology and applications of multivariate analysis; Hotelling's T2; multivariate regression and analysis of variance; classification and discrimination; principal components, clustering, and multidimensional scaling; use of statistical software. Offered: Spring BST 450 Data Analysis Prerequisites: BST 426 and BST 477 or BST 478 Description: Statistical analysis of data under nonstandard conditions; examination of adequacy of model assumptions; goodness-of-fit testing; transformations; robust inference. BST 451 Exploratory Data Analysis Prerequisites: BST 416 or BST 476 and BST 478 Description: Graphical techniques to reveal structure in data; model fitting to describe structure; model checking; transformations; outliers and resistant fitting methods. BST 452 Design of Experiments Prerequisites: BST 426 and BST 477 or BST 478 Description: Completely randomized designs; replication; covariate adjustment; randomized block designs; fixed vs. random effects; Latin and Graeco-Latin squares; confounding; nesting; factorial and fractional factorial designs; split-plot designs; incomplete block designs; response surfaces. BST 463 Introduction to Biostatistics Restrictions: Permission of instructor required for undergraduates Description: Introduction to statistical techniques with emphasis on applications in the health sciences. Summarizing and displaying data; introduction to probability; Bayes' theorem and its application in diagnostic testing; binomial, Poisson, and normal distributions; sampling distributions; estimation, confidence intervals, and hypothesis testing involving means and proportions; simple correlation and regression; contingency tables; use of statistical software. Offered: Fall BST 464 Applied Linear Regression Restrictions: Permission of instructor required for undergraduates Prerequisites: BST 463 or equivalent Description: One-way and two-way analysis of variance; multiple comparisons involving means; fixed and random effects; simple and multiple linear regression; analysis of covariance; interactions; correlation and partial correlation; multicollinearity; model selection; model checking. Offered: Fall BST 465 Design of Clinical Trials Restrictions: Permission of instructor required for undergraduates Prerequisites: BST 463 or equivalent Description: Introduction to the principles of clinical trials; clinical trial protocols; overview of the drug development process; hypotheses/objectives; specification of response variables; defining the study population; randomization; blinding; ethical issues; factorial designs; crossover designs; equivalence trials; trial monitoring and interim analyses; sample size and power; issues in data analysis and reporting; evaluating clinical trial reports. Offered: Spring BST 466 Categorical Data Analysis Restrictions: Permission of instructor required for undergraduates Prerequisites: BST 464 or equivalent Description: Measures of association for categorical outcomes; contingency table analysis; regression analysis for binary, polytomous, count and time-to-event responses; emphasis on general ideas and applications of models and methods using statistical software such as SAS; review of necessary theory underlying likelihood and nonparametric inference as it pertains to the development of relevant models and test statistics. Offered: Spring BST 467 Applied Statistics in the Biomedical Sciences Restrictions: Permission of instructor required for undergraduates Description: Experimental design, statistical inference, hypothesis testing, linear and non-linear regression analysis and model diagnosis, analysis of time-to-event data, sample size and power calculation, and genomic data analysis. Offered: Spring BST 476 Introduction to Linear Models Prerequisites: STT 203 or STT 212 or BST 463 Description: Simple and multiple regression models; least-squares estimation; hypothesis testing; interval estimation; prediction; matrix formulation of the general linear model; polynomial regression; analysis of variance; analysis of covariance; methods for simultaneous inference; residual analysis and checks of model adequacy. Offered: Fall BST 477 Introduction to Statistical Software I Restrictions: Open only to graduate students in offering department Prerequisites: STT 212 or BST 463 Description: Introduction to a statistical software package. The software to be introduced may vary from semester to semester; a common choice is SAS. Generally offered during the first 6 weeks of the summer. Credit - none. BST 478 Introduction to Statistical Software II Restrictions: Open only to graduate students in offering department Prerequisites: STT 212 or BST 463 Description: Introduction to a statistical software package. The software to be introduced may vary from semester to semester; a common choice is S-Plus. Generally offered during the first 6 weeks of the summer. Credit - none. BST 479 Generalized Linear Models Prerequisites: BST 411 and BST 426 Description: Generalized linear models; computational techniques for model fitting; logistic and conditional logistic regression; log-linear models; models for nominal and ordinal categorical data; quasi-likelihood functions; model checking; introduction to semiparametric generalized linear models. Offered: Fall BST 487 Seminar in Statistical Literature Description: 1 credit Offered: Fall and Spring BST 491 Reading Course at the Master's Level Description: Credit varies BST 493 Internship/Applied Project Description: As required for completion of the M.S. degree in medical statistics, the student works on a medical research project under the guidance of department faculty or under supervision in an industrial setting. The student should have contact with medical investigators as well as statisticians. The work should be coherently summarized in a written document. Oral presentation of the work is required. Offered: Fall / Spring / Summer BST 495 Research at the Master's Level Description: Credit varies BST 496 Wet/Dry Lab Rotation Description: Students will choose a bioinformatics experimental or computational lab for rotations. BST 511 Topics in Statistical Inference I Prerequisites: Varies by topic Description: Advanced topics in statistical inference and/or decision theory. Recent topics include: Bayesian Inference Smoothing Methods Frailty Models Permutation Tests The Bootstrap, The Jackknife, and Resampling Methods Offered: Fall BST 512 Topics in Statistical Inference II Prerequisites: Varies by topic Description: Advanced topics in statistical inference and/or decision theory. Recent topics include: Bayesian Inference Smoothing Methods Frailty Models Permutation Tests The Bootstrap, The Jackknife, and Resampling Method Offered: Spring BST 513 Analysis of Longitudinal and Dependent Data Prerequisites: BST 401 and BST 411 and BST 426 Description: Modern approaches to the analysis of longitudinal and dependent data; random and mixed effects models; marginal models; generalized estimating equations; models for continuous and discrete outcomes. Offered: Spring BST 514 Survival Analysis Prerequisites: BST 411 and BST 412 or BST 402 Description: Parametric, nonparametric, and semiparametric methods for the analysis of survival data. Right censoring; Kaplan-Meier curves; log-rank and weighted log-rank tests; survival distributions; accelerated life and proportional hazards regression models; time-dependent covariates; partial likelihood; models for competing risks and multiple events. Offered: Fall BST 520 Current Topics in Bioinformatics Description: Basic concepts of modern molecular biology; bioinformatics technologies; sequence analysis of nucleic acids and proteins (methods of sequence alignment and associated search algorithms); prediction of structure and functions: protein folding and RNA secondary structure; statistical methods for microarray gene expression data analysis: (1) univariate methods for selecting differentially expressed genes (SAM, step-down and step-up resampling methods, empirical Bayes method) and (2) multivariate methods for identifying subsets of differentially expressed genes and pathway recognition (distance-based and error-based approaches, successive selection of subsets of genes, testing significance in multivariate settings); selection bias in multivariate analysis and cross-validation of classification rules; Support Vector Machines in the analysis of microarrays; unsupervised learning with microarray data; identification of gene regulatory networks from gene perturbation experiments; prognostic value of molecular signatures of cancer cells; common pitfalls in gene expression data analysis and a critical overview of the existing methods; methods for analysis of complex genetic traits and gene finding in genetic epidemiology; promising avenues for future statistical research in the field of bioinformatics. Offered: Spring BST 521 Advanced Computing for Bioinformatics and Computational Biology Prerequisites: Calculus Description: Contents include numerical optimization methods, numerical splines and interpolation, numerical algorithms for differential equations, Monte Carlo methods, parallel computing, and selected application topics. BST 522 Big Data in Biomedical Research Prerequisites: BST 411 and BST 435 Description: This course will introduce the big data concepts and research issues in biomedical research. The contents include: 1) Introduction to Big Data concepts. 2) Identifying and locating relevant data: public databases and data repositories. 3) Data warehouse: manage and organize the Big Data. 4) Big Data standardization, processing, and analysis. 5) Data mining and pattern recognition. 6) Big Data integration and modeling. BST 523 Dynamic Modeling for Biological Processes Prerequisites: BST 431 Description: The following topics will be in this course: 1) An overview of dynamic models 2) Useful linear algebra techniques 3) Ordinary differential equations 4) Partial differential equations 5) Useful techniques for Markov chains 6) Discrete-time dynamical systems 7) Continuous-time dynamical systems 8) Cellular dynamics and pathways of gene expression 9) ODE models for infectious diseases 10) Spatial patterns and reaction-diffusion PDE models. BST 525 Introduction to Health Informatics Restrictions: Permission of instructor required Prerequisites: Health sciences (medical, nursing, public health, etc.) background or technical (computer science, information science, statistics, etc.) background Description: Introduction to health informatics; clinical data and biomedical knowledge; electronic medical records and integrated health care information systems; standards for health information technology; natural language and text processing/information retrieval; human factors in health informatics; translational informatics and decision support systems; public health informatics, telemedicine, and patient monitoring; evaluation of health care information systems; consumers, web, and health education. BST 526 High-Dimensional Bioinformatics Data Analysis and Inference Prerequisites: BST 411 and BST 426 Description: Contents include: 1) High-dimensional linear regression models 2) Linear methods for classification 3) Basis expansions and regularization 4) Kernel smoothing methods 5) Model assessment and selection 6) Model inference and averaging 7) Additive models, trees, and related methods 8) Boosting and additive trees 9) Support vector and flexible discriminants 10) Prototype methods and nearest-neighbors 11) Unsupervised learning methods, such as principal component analysis (PCA), cluster analysis, multidimensional scaling, and self-organizing map. BST 527 Networks and Graphical Models in Genomic Applications Prerequisites: BST 411, BST 432, and BST 433 Description: Contents include: 1) Systems biology: biological networks and their properties (connectivity, modularity; power low; clustering; network motifs) 2) Introduction to graph theory 3) Measures of co-expression, correlation structures, and statistical methods. 4) Relevance networks. 5) Probabilistic graphical models: Bayesian Networks, Markov Networks. 6) Boolean networks. BST 531 Nonparametric Inference Prerequisites: BST 411 and BST 426 Description: Nonparametric estimation and inference for one-sample location and paired data, two-sample location and/or dispersion, one- and two-way layouts with and without order restrictions, tests of independence, and regression; exact and large-sample results for some commonly used procedures, including the sign test and the sample median, the Mann-Whitney-Wilcoxon test and the Hodges-Lehmann location measure, and some generalizations to more complex data structures; density estimation; nonparametric regression; generalized additive models (GAM); cross-validation; bandwidth selection; exact and asymptotic bias, variance, and mean squared error (MSE). BST 536 Sequential Analysis Prerequisites: BST 412 Description: The Wald sequential probability ratio test and generalizations; tests of composite hypotheses; nonparametric sequential procedures; sequential estimation and confidence intervals; Brownian-motion based sequential methods, with applications to clinical trials; group sequential methods; optimal stopping rules. BST 541 Multivariate Analysis Prerequisites: BST 411 and BST 426 Description: Multivariate normal and Wishart distributions and associated distributions; estimation; invariance reduction; Hotelling?s T2; multivariate general linear model; simultaneous confidence bounds; step down procedures; optimality properties; classification; discrimination; principal components. BST 550 Topics in Data Analysis Restrictions: Permission of instructor required Description: Advanced statistical methods for data analysis. BST 570 Topics in Biostatistics Restrictions: Permission of instructor required Description: Advanced biostatistical techniques. BST 582 Introduction to Statistical Consulting Description: Formal instruction on developing and managing consulting relationships. BST 590 Supervised Teaching Description: One to two classroom hours per week of discussion and problem solving with University of Rochester students, under the guidance of a member of the faculty. BST 591 Reading Course at the PhD Level Description: Special work for doctoral candidates, arranged individually. BST 592 Supervised Statistical Consulting Description: Supervised consulting with medical and other scientific researchers under the guidance of a member of the faculty. BST 595 Research at the PhD Level Description: Credit varies Smoothing Methods (BST 511 and BST 512) Prerequisites: BST 412, BST 426, and BST 478 Description: The course will cover 3 main topics: (1) density estimation methods, including histograms, frequency polygons, kernel density estimators, local likelihood density estimators, and penalized likelihood and spline-based estimators; (2) nonparametric regression, with an emphasis on local polynomial modeling and some discussion of cubic smoothing splines; and (3) generalized additive models (GAM). Attention will be paid to locally varying smoothing parameters, boundary effects and corrections, consistency, rates of convergence, extensions to higher dimensions and the "curse of dimensionality," limit distributions, smoothing parameter selection, and kernel choice, including higher-order and equivalent kernels. Frailty Models in Survival Analysis (BST 511 and BST 512) Prerequisites: BST 411, BST 479 or BST 514 Description: The notion of frailty provides a convenient way to introduce random effects, association and unobserved heterogeneity into models for survival data. In its simplest form a frailty is an unobserved random proportionality factor which modifies the hazard function of an individual, or of related individuals. In essence the concept goes back to the 1920 work of Greenwood and Yule on "accident proneness." The term frailty itself was introduced by Vaupel, Manton and Stallard in 1979 and applications in survival analysis were popularized in a series of papers by P. Hougaard. Applications to multivariate survival data date from a seminal 1978 paper by D. Clayton. The course will provide a general introduction to frailty models for univariate and multivariate survival data and for repeated events. We will discuss the formulation of frailty models and identifiability aspects, connections with two-sample rank tests for survival data and with measures of association for bivariate survival data. Parametric and semiparametric methods of fitting frailty models will be reviewed, including the use of the EM algorithm and related approaches including hierarchical likelihood. Extensions to correlated frailty models will also be described. The distinction between "conditional models," in which the effect of observed covariates is described conditionally on the value of the random effect and "marginal models," which integrate over the unobserved effect, will be emphasized. Classical survival analysis methodology, including the Kaplan-Meier estimator and Cox's regression model, will be reviewed briefly at the start of the course. The Bootstrap, The Jackknife, and Resampling Methods (BST 511 and BST 512) Prerequisites: BST 412 and BST 478 Description: Bootstrap methods, including the nonparametric, parametric, smoothed, m-out-of-n, and randomly weighted bootstrap procedures, will be presented for estimating standard errors, constructing various types of confidence intervals, performing hypothesis tests, and estimating bias. One- and two-sample problems, regression, correleted data, and more general inference problems will be considered. Jackknife and cross-validation methods will also be discussed.