## Courses

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**STAT 500 M.S.Thesis NC**

Program of research leading to M.S. degree arranged between student and faculty member. Students register to this course in all semesters starting from the beginning of their second semester while the research program or write-up of thesis is in progress.

**STAT 504 Nonparametric Statistical Inference and Methods (3-0)3**

Use of order statistics and other distribution-free statistics for estimation and hypothesis testing, exact non-parametric tests and measures of rank correlation. Relative efficiency, asymptotic relative efficiency and normal-score procedures. Test of goodness of fit.

Prerequisite: STAT 572.

**STAT 505 Sampling Theory and Methods (3-0)3**

General randomization theory of simple and multistage sampling, sampling with and without replacement and with equal and unequal probabilities, ratio and regression estimates, analytical studies and multiframe problems in relation to stratification, systematic sampling, clustering and double sampling.

**STAT 509 Applied Stochastic Processes (3-0)3**

Markov chains, discrete and continuous Markov processes and associated limit theorems. Poisson and birth and death processes. Renewal processes, martingales, Brownian motion, branching processes. Weakly and strongly stationary processes, spectral analysis. Gaussian systems.

Prerequisite: Advanced Calculus, Probabilitiy Theory.

**STAT 510 Research Methods and Ethics in Statistics NC**

Research design in the field of statistics following ethical standards, ethical issues in scientific research, how to write a thesis with ethics, journal types, publication types, citations, plagiarism, how to be a graduate student, how to be a researcher.

**STAT 518 Statistical Analysis of Designed Experiments (3-0)3**

Randomization theory of experimental design. Principles of blocking. General analysis of experimental design models. Construction and analysis of balanced and partially balanced complete and incomplete block designs. Factorial design: confounding, aliasing, fractional replication. Designs for special situations.

Prerequisite: STAT 572

**STAT 525 Regression Theory and Methods (3-0)3**

General regression models, residual analysis, selection of regression models, response surface methods, nonlinear regression models, experimental design and analysis of covariance models. Least squares, Gauss-Markov theorem. Confidence, prediction and tolerance intervals. Simultaneous inference, multiple comparison procedures.

**STAT 529 Statistical Bioinformatics (3-0)3**

Definition of certain fundamental biological and chemical processes, principles of probability and statistics, microarray analyses, fundamental and advanced classification and clustering methods, analyses of protein sequence alignments, structure and elements of biological network, visualization tools and databases in bioinformatics.

**STAT 542 Seminar I NC**

Seminar course for M.S. students in Statistics.

**STAT 543 Seminar II NC**

M.S. students prepare and present a seminar in their thesis topic.

**STAT 545 Longitudinal Data Analysis (3-0)3**

Introduction to longitudinal / panel data. Missing cases in longitudinal data. Exploratory longitudinal data analysis. Marginal models, transition models, random effects models, multilevel (hierarchical) models. Estimation methods for this type of data.

**STAT 553 Actuarial Analysis and Risk Theory (3-0)3**

Basics of insurance; Basics of reinsurance; Non-life insurance mathematics; Insurance economics; Risk theory; Individual and collective risk models; Ruin theory; Credibility theory and applications.

**STAT 554 Computational Statistics (3-0)3**

Overview of statistical distributions, generating random variables, exploratory data analysis, Monte Carlo (MC) method for statistical inference, data partitioning, resampling, bootstrapping, nonparametric density estimation.

**STAT 557 Statistical Modeling I (3-0)3**

Introduction to the general theory of linear models, least squares and maximum likelihood estimation. Introduction to non-linear, log-linear and generalized linear models. Logistic and Poisson regression, ordinal and multinomial logit models. ANOVA. Causation versus association. Introduction to special Statistical Models, such as Time Series Models, Actuarial Models, Survival Models, Reliability Models.

**STAT 558 Statistical Modeling II (3-0)3**

Bayesian models, hierarchical modeling, nonparametric regression models, semi- parametric models, random and mixed models, response surface methods, residual analysis, correlation analysis, experimental design and analysis of covariance models.

**STAT 559 Applied Multivariate Analysis (3-0)3**

Characterizing and displaying multivariate data, multivariate distributions, tests of mean vectors and covariate matrices, discriminant analysis, classification and pattern recognition, canonical correlation, principle component analysis, factor and cluster analysis, multivariate linear, random and mixed models, multidimensional scaling.

**STAT 560 Logistic Regression Analysis (3-0)3**

Introduction to categorical response data. Fitting logistic regression models. Interpretation of coefficients. Maximum likelihood estimation. Hypothesis testing. Model building and diagnostics. Polytomous logistic regression. Interaction and confounding. Logistic regression modelling for different sampling designs: case-control and cohort studies, complex surveys. Conditional logistic regression. Exact methods for small samples. Power and sample size. Recent developments in logistic regression approach.

**STAT 562 Univariate Time Series Analysis (3-0)3**

Fundamental concepts in univariate time domain analyses, properties of autocovariance and autocorrelation of time series, stationary and nonstationary models, difference equations, autoregressive integrated moving average processes, model identification, parameter estimation, model selection, time series forecasting, seasonal time series models, testing for a unit root, intervention analysis, outlier detection, handling missing observations in time series, Fourier series, spectral theory of stationary processes and the estimation of the spectrum.

**STAT 563 Multivariate Time Series (3-0)3**

Transfer function models and cross-spectral analysis, time series regression and GARCH models, vector time series models, error-correction models, cointegration and causality, state space models and Kalman filter, long memory processes, nonlinear processes, temporal aggregation and disaggregation.

**STAT 564 Advanced Statistical Data Analysis (3-0)3**

Introduction to methods for analyzing experimental and observational data. Useful display of univariate and multivariate data. Exploratory data analysis. Transforming data. Detecting and handling outliers. Examining residuals. Resistant lines. Robust estimation. Approaches to handling missing data. Analysis of categorical data. Data mining.

**STAT 565 Decision Theory and Bayesian Analysis (3-0)3**

Introduction to decision making. Subjective and frequentist probability. Bayes theorem and Bayesian decision theory. Advantages of using a Bayesian approach. Likelihood principle, prior and posterior distributions, conjugate families. Inference as a statistical decision problem. Bayesian point estimation, Tests and confidence regions, model choice, invariance, equivariant estimators, hierarchical and empirical Bayes extensions, robustness and sensitivity, utility and loss, sequential experiments, Markov Chain Monte Carlo Methods, Metropolis-Hastings Algorithm, Gibbs Sampling, The E-M Algorithm.

**STAT 566 Reliabiliy Theory and Methods (3-0)3**

Introduction to reliability, order statistics, censoring and likelihood, nonparametric estimation, extreme value theory, failure time distributions, parametric likelihood concepts, simulation-based methods, testing reliability hypothesis, system reliability, failure-time regression analysis, accelerated life testing.

**STAT 567 Biostatistics and Statistical Genetics (3-0)3**

Introduction to use of statistical methodology in health related sciences. Types of health data. Odds ratio, relative risk. Prospective and retrospective study designs. Cohort, case-control, matching case-control, case-cohort, nested case-control studies. Analysis of survival data. Kaplan-Meier, life tables, Cox's proportional hazards model. Analysis of case-control data. Unconditional, conditional, polytomous logistic regression. Introduction to genetic epidemiology. Testing Hardy-Weinberg law. Linkeage analysis. Analysis of microarray data. Association studies. Sample size and power. Recent developments in biostatistics and genetic epidemiology.

**STAT 568 Statistical Consulting (3-0)3**

Key aspects of statistical consulting and data analysis activities. Formulation of statistical problems from client information. Analysis of complex data sets. Case studies. Writing and presenting reports.

**STAT 570 Data Handling and Visualization (3-0)3**

Structured, semi-structured and unstructured data types. Data manipulation and preprocessing. Dimension reduction. Sampling, oversampling, undersampling. Data scraping and wrangling. Visualization of multivariate data. Panel displays, surface plots, 3D scatterplots, contour plots. 2D representation of multivariate data. Interactive graphics revealing any structure in data: Asimov’s grand tour, projection pursuit explanatory data analysis (PPEDA). Visualization of categorical data. Dynamic graphics.

**STAT 571 Data Mining and Machine Learning (2-2)3 (MUST)**

Unsupervised learning. Principal component analysis (PCA), clustering methods. Rule learning, association rules. Supervised learning. Multiple linear regression. K-nearest neighbors. Logistic regression. Linear discriminant analysis. Linear model selection. Regularization techniques. Ridge regression, LASSO. Splines. Generalized additive models (GAMs). Tree-based methods. Ensemble learning. Bagging, random forest, boosting. Support vector machines. Neural networks and deep learning. Evaluating the performance of machine learning algorithms. No Free Lunch theorems. Bias-variance decomposition. Bagging. Boosting. Generative adversarial networks (GANs). Autoencoders. Variational Autoencoders.

**STAT 572 Probability and ****Statistics for Data Science I (3-0)3 (MUST)**

Introduction to history and concepts of probability, statistics and data science, artificial intelligence, data mining, machine learning, deep learning, comparison of these topics, probability, combinatorics, random variables, some common discrete and continuous distributions and their properties, expectations, joint distribution functions, conditional distributions, distribution functions, moment generating functions, transformations of variables, multivariate normal distribution, limit theorems.

**STAT 573 Probability and ****Statistics for Data Science**** II (3-0)3 (MUST)**

Order statistics. Likelihood functions and likelihood theory. Exponential families. Point estimation. Some properties of estimators. Interval estimation. Hypothesis testing.

**STAT 574 Statistics and Data Science Computing (3-0)3**

Computer arithmetic, matrices and solving linear equations, regression computations, Eigen problems, interpolation, smoothing and approximation, maximum likelihood and nonlinear regression, numerical integration and Monte Carlo (MC) methods.

**STAT 575 Computational Tools for Data Science (2-2)3**

Programming with R and Python for statistics and data science computing. Computing using statistical software. Relational, distributed, parallel and object databases. Structured query language (SQL). Big data storage systems. Data warehouses. Online analytic processing (OLAP). Big data handling tools and techniques. Web data management. Cloud computing.

**STAT 576 Neural Networks for Data Science (3-0)3**

Basics of neural network (NN) computing. AI problem solving, and Von Neumann architecture. Important neural network models. Adaline and Perceptron; feedforward, feedback, recurrent and self-organizing and thermodynamic networks. Learning methods. Hebbian, perceptron, back-propagation learning and unsupervised competitive learning. Hopfield Network, Data preprocessing: principal and independent component analysis. Practical applications of these techniques in Data Science.

**STAT 577 Big Data Analytics (3-0)3**

Data wrangling and scraping. Clusters for computing. Clouds for storage. Tools for big data analytics. Hadoop, Spark, Tensorflow. Applications of big data analytics. Stream data processing. Large data visualization. Social network analysis and text mining.

**STAT 578 Artificial Intelligence and Data Science (3-0)3**

Problem solving. Searching. Logic in AI. Knowledge representation. Common sense reasoning. Probabilistic reasoning. Making complex decisions. Planning and scheduling. Expert systems. Learning from examples. Statistical learning. Reinforcement learning. Neural networks and deep learning. Natural Language Processing (NLP). Statistical pattern recognition. Robotics. Computer vision. Speech understanding. Machine translation. Perception. Explainable AI. Next generation AI technology.

**STAT 579 Statistical Pattern Recognition (3-0)3**

Bayesian decision analysis. Supervised learning methods: neural networks, linear discriminant analysis, kernel methods, regression and model tree algorithms, nearest neighbor. Unsupervised learning methods: flat and hierarchical clustering, and graphical models.

**STAT 580** **Stochastic Processes in Machine Learning ****(3-0)3**

This course intent to introduce Hidden Markov Models (HMMs) which are commonly used for modelling stochastic behaviour of dynamic systems and mainly cover concepts related to HMMs with a formulation appropriate for filtering and parameter estimation.

**STAT 598 Term Project in Statistics NC**

A project is carried out under the supervision of a faculty member in a specified area of Statistics. Students are required to write a report about their work.

**STAT 600 Ph.D. Thesis NC**

Program of research leading to Ph. D. degree arranged between student and faculty member. Students register to this course in all semesters starting from the beginning of their second semester while the research program or write-up of thesis is in progress.

**STAT 601 Advanced Probability Theory I (3-0)3**

Notions of measure theory. General concepts and tools of probability theory. Independence; convergence; laws of large number. Random walks.

**STAT 602 Advanced Probability Theory II (3-0)3**

Concept of conditioning. From independence to dependence. Ergodic theorems. Martingales and decomposibility. Brownian motion and limit distributions.

**STAT 603 Advanced Theory of Statistics I (3-0)3**

Advanced topics in linear and non-linear statistical estimation.

**STAT 604 Advanced Theory of Statistics II (3-0)3**

Advanced topics in statistical hypothesis testing.

**STAT 605 Theory of Linear and Nonlinear Statistical Models (3-0)3**

General linear and nonlinear models. Topics related to the statistical inference in model building. Prerequisite: Consent of instructor.

**STAT 606 Theory of Experimental Designs (3-0)3**

Balanced and partially balanced incomplete block designs. Mixture designs. Factorial designs. Response surfaces. Optimal allocation of observations. Prerequisite: Consent of instructor.

**STAT 607 Nonparametric Theory of Statistics (3-0)3**

Rank testing and estimation procedures. Locally the most powerful rank tests. Criteria for unbiasedness. Exact and asymptotic distribution theory. Asymptotic efficiency. Rank correlation. Sequential procedures. Prerequisite: Consent of instructor.

**STAT 608 Probability Models and Stochastic Processes (3-0)3**

Discrete and continuous time Markov chains and Brownian motion. Gaussian processes, queues, epidemic models, branching processes, renewal processes.

**STAT 609 Statistical Decision Theory (3-0)3**

Decision theoretic approach to statistical problems. Complete class theorems. Bayes and minimax procedures. Multiple, sequential, invariant statistical decision problems. Prerequisite: Consent of instructor.

**STAT 610 Sequential Analysis (3-0)3**

Sequential probability ratio test. Approximations for stopping boundaries. Power curve and expected stopping time. Wald's lemmas. Bayes character of SPRT. Composite hypothesis. Ranking and selection Prerequisite. Consent of instructor.

**STAT 611 Multivariate Analysis (3-0)3**

Advanced topics in multivariate statistical analysis. Prerequisite: Consent of instructor.

**STAT 612 Advanced Topics in Time Series Analysis (3-0)3**

Univariate and multivariate time series analysis. Estimation and hypothesis testing in the time and frequency domains. Prerequisite: Consent of instructor.

**STAT 613 Advanced Topics in Life Testing and Reliability (3-0)3**

Advanced topics in life models, reliability and hazard functions. Decision making in life testing. Design of experiments in life testing. Prerequisite: Consent of instructor.

**STAT 614 Interpretation of Data (3-0)3**

Application of statistical theory and procedures to various types of data. Use of computers and numerical methods are emphasized. Prerequisite: Consent of instructor.

**STAT 615 Interpretation of Data II (3-0)3**

Continuation of STAT 614.

**STAT 616 Applications of Statistics in Industry (3-0)3**

A strong background in control charts including adoptations, acceptance sampling for attributes and variables data. Acceptance plans. Statistics of combinations. Prerequisite: Consent of instructor.

**STAT 617 Large Sample Theory of Statistics (3-0)3**

Large sample properties of tests and estimates. Problems of consistency and various forms of asymptotic efficiencies. Irregular estimation problems. Inference from stochastic processes. CCH: (1-0)1. Prerequisite: Consent of instructor.

**STAT 618 Mathematical Models and Response Surface Methodology (3-0)3**

Two level factorial and fractional factorial designs, blocking, polynomial models, first order and second order designs, several responses, determination and optimum conditions, design criteria involving variance and bias. CCH: (1-0)1. Prerequisite: Consent of instructor.

**STAT 619 Advanced Topics in Regression and Analysis of Variance (3-0)3**

Development of linear classification models, components of variance for balanced designs, polynomial models, harmonic regression, crossed models for combined qualitative and quantitative factors. Analysis of variance for fixed, random and mixed effects models. Randomization. Violation of assumptions. CCH: (1-0)1. Prerequisite: Consent of instructor.

**STAT 620 Bayesian Inference (3-0)3**

Sampling theory, subjective probability, likelihood principles. Bayes theorem, Bayesian analysis of normal theory, inference problems, assessment of model assumptions, robustness of inference, analysis of variance, some aspects of multivariate problems. Bayesian aspects of statistical modelling. CCH: (1-0) 1. Prerequisite: Consent of instructor.

**STAT 621 Robust Statistics (3-0)3**

Transforming data. More refined estimators. Comparing location estimators. M and L estimators. Robust scale estimators and confidence intervals. Relevance to hypothesis testing. CCH: (1-0)1. Prerequisite: Consent of instructor.

**STAT 622 Discrete Multivariate Analysis (3-0)3**

Structural models for counted data, maximum likelihood estimates for complete tables, formal goodness of fit; summary statistics and model selection, maximum likelihood estimates for incomplete tables, estimating the size of a closed population, models for measuring change, analysis of square tables; symmetry and marginal homogeneity, measures of association and agreement, Pseudo-Bayes estimates of cell probabilities, asymptotic methods. CCH: (1-0)1. Prerequisite: Consent of instructor.

**STAT 623 Spatial Statistics (3-0)3**

Purely spatial processes. Spatial autocorrelation. Distribution theory for spatial statistics. Analysis for point patterns. Parametric spatial models. Estimation and testing procedures.

**STAT 630 Advanced Topics in Statistical Inference (3-0)3**

Several advanced topics of statistical inference suited to the needs of researcher. Prerequisite: Consent of instructor.

**STAT 632 Inference for Stochastic Processes (3-0)3**

Special models. Large sample theory for discrete and continuous parameter stochastic pocesses. Optimal testing. Bayesian, nonparametric and sequential inference for stochastic processes. Martingales. Stochastic differential equations

**STAT 634 Theory of Stationary Random Functions (3-0)3**

Second moment models of random variables and vectors. Correlation theory of random processes in the time and frequency domains. Theory of random fields in the time and frequency domains. Crossings and extremes of random functions. Applications. Prerequisite: Consent of instructor.

**STAT**** 635 Advanced Computational Statistics (3-0)3 (MUST)**

Exploring multidimensional data. Discovering structure in data. Bootstrapping basics and dependent data. Data partitioning. Statistical pattern recognition: classifiers and clustering. Bivariate and multivariate smoothing. Nonparametric regression models. Advanced topics in Markov Chain Monte Carlo (MCMC).

**STAT 636 ****Advanced Generalized Linear Models (3-0)3 (MUST)**

Review of matrix algebra. A theoretical development of generalized linear models. Estimation, interpretation and inferences for generalized linear models for responses from different distributions, such as Gaussian, Binomial, Poisson. Loglinear models. Penalized estimation.

**STAT 637**** Spatial Data Analysis (3-0)3**

Modeling data with spatial structure, geostatistical data, random fields; variograms, covariance, stationarity, kriging, areal data, spatial regression, SAR, CAR, QAR, MA models, Geary/Moran indices, point patterns, G, F, K, L functions, complete spatial randomness; homogeneous/inhomogeneous processes, marked point processes, spatio-temporal modeling, visualization of spatial data. The programming language R and a few packages for analyzing spatial data will also be introduced.

**STAT 638 Computation and Optimization (3-0)3**

Optimization and solving nonlinear equations. Combinatorial optimization: tabu, simulated annealing, genetic algorithms. Expectation-maximization (EM) optimization. Simulation and Monte Carlo (MC) integration. Markov Chain MC (MCMC) methods.

**STAT 639 Stochastic Differential Equations (3-0)3**

This is an introductory stochastic calculus and stochastic differential equations course which will cover fundamental concept in the areas of stochastic calculus in finance, population models and such.

**STAT 640 Advanced Statistical Consulting (3-0)3**

Key aspects of statistical consulting. Emphasis on communication and selecting the appropriate statistical methods. Extensive computations using a statistical software. Analysis of complex data sets. Case studies. Writing and presenting reports.

**STAT 641 Ethics in Data Science (3-0)3**

Ethics in statistical practice. Social impacts of algorithmic methods of data science.

**STAT 642 Seminar in Statistics and Data Science I NC**

Seminar course for Ph.D. students in Statistics.

**STAT 643 Seminar in Statistics and Data Science II NC**

Ph.D. students prepare and present a seminar in their thesis topic.

**STAT 645 Statistical Deep Learning (3-0)3**

The focus of this course will be on understanding deep neural networks by connecting it to related concepts in statistics. Topics treated include feedforward networks, regularization and optimization of networks with many layers, convolutional networks, recurrent networks and validation methods. In addition, mathematical interpretations of networks are given, explainability methods are presented, how to explain the network performance, and how to deal with adversarial attacks. The course includes some of the following unsupervised learning topics; autoencoders, representation learning, deep generative methods, and information theoretic concepts of deep learning. Applications with Python-based deep learning development frameworks will be used in practical applications of these techniques in Data Science and Analytics.

**STAT 646 Statistical Inferences for Stochastic Processes (3-0)3**

Introduction to Stochastic models and examples; Special models; Discrete and continuous time Markov chains and Brownian motion; Large sample theory for discrete and continuous parameter stochastic processes; Bayesian, nonparametric and sequential inference for stochastic processes; Gaussian processes; Queues; Epidemic models; Branching processes; Renewal processes.

**STAT ****647 Probability Theory (4-0)4 (MUST)**

This is an introductory measure-theoretic probability theory course. We will be covering the fundamental concepts in Statistics to the full extent, such as Law of Large Numbers, Central Limit Theorem, Convergence, Dependence, Independence, Conditional Expectation. The course covers all the content that appear on the Probability Qualification Examination.

**STAT**** 648 ****Advanced Statistical Inference (4-0)4 (MUST)**

Theory of likelihood based estimation, likelihood construction for advance models, theory of robust estimation, theory of hypothesis testing

**STAT 699 Ph.D. Thesis in Statistics NC**

**STAT 800-899 Special Studies NC**

**STAT 900-999 Special Topics NC**

*** NC: Non-Credit**