**STAT 500 Statistical Methodology in Archaeometry**

Subjects covering statistical methodology in collectingband analyzing data. Elementary probability distributions, hypothesis testing, analysis of variance, analysis of frequencies with emphasis on the use of computers in processing data. (Open to the students of the Archaeometry Program).

**STAT 501 STATISTICAL THEORY I**

Probability, random variables, expectations, joint distribution functions, conditional distributions, distribution functions, moment generating functions, order statistics, censoring, limit theorems, multivariate normal distribution.

**STAT 502 STATISTICAL THEORY II**

Likelihood theory, sufficiency, point estimation, methods of estimation, unbiasedness, Delta method, hypothesis testing, interval estimation, asymptotic theory, Bayesian statistics, loss function, inference for bivariate distributions.

**STAT 504 Nonparametric Statistical Inference and Methods**

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. CCH:(1-0) 1. *Prerequisite: STAT 501.*

**STAT 505 Sampling Theory and Methods**

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. CCH: (1-0) 1. *Prerequisite: equivalent of STAT 351-352.*

**STAT 509 Applied Stochastic Processes**

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. CCH:(1-0)1. *Prerequisite: Advanced Calculus, Probabilitiy Theory and equivalent of STAT 351-352.*

**STAT 518 Statistical Analysis of Designed Experiments**

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. CCH: (1-0)1. *Prerequisite: STAT 501 and STAT 503.*

**STAT 525 Regression Theory and Methods**

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. CCH: (1-0)1.

**STAT 551 PROBABILITY AND STATISTICS I**

Probability, combinatorics, random variables, expectations, joint distribution functions, conditional distributions, distribution functions, moment generating functions, limit theorems.

**STAT 552 PROBABILITY AND STATISTICS II**

Order statistics, exponential families, sufficiency, point estimation, hypothesis testing, interval estimation, confidence intervals.

**STAT 553 Actuarial Analysis and Risk Theory**

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**

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 555 ADVANCED COMPUTATIONAL STATISTICS**

Bivariate and multivariate smoothing, discovering structure in data, nonparametric regression, Markov Chain Monte Carlo (MCMC), statistical pattern recognition: classifiers and clustering.

**STAT 556 ADVANCED COMPUTING METHODS IN STATISTICS**

This course introduces a range of computational techniques that are important to Statistics. The topics covered include introduction to statistical computing, computer arithmetic, numerical linear algebra, regression computations, eigenproblems, numerical optimization, numerical approximations, numerical integration, expectation-maximization (EM) algorithm, basic simulation methodology, Monte Carlo (MC) integration, MC Markov Chain (MCMC) methods.

**STAT 557 STATISTICAL MODELING I**

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**

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**

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**

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 561 PANEL DATA ANALYSIS**

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

**STAT 562 UNIVARIATE TIME SERIES ANALYSIS**

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 ANALYSIS**

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**

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**

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 RELIABILITY THEORY AND METHODS**

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**

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**

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 542 Seminar in Statistics (Non-credit)**

Seminar course for M.S. students in Statistics.

**STAT 599 M.S. Thesis in Statistics (Non-credit)**

**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. *Prerequisite: Consent of instructor.*

**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. *Prerequisite: Consent of instructor.*

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

Advanced topics in linear and non-linear statistical estimation.* Prerequisite: Consent of instructor.*

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

Advanced topics in statistical hypothesis testing. *Prerequisite: Consent of instructor.*

**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 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. *Prerequisite: Consent of instructor.*

**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 CCH: (1-0)1. *Prerequisite. Consent of instructor.*

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

Advanced topics in multivariate statistical analysis. CCH: (1-0)1 *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. CCH: (1-0)1. *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. CCH:(1-0)1. *Prerequisite: Consent of instructor.*

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

Application of statistical theory and procedures to various types of data. Use of computers and numerical methods are emphasized. CCH: (1-0)1. *Prerequisite: Consent of instructor.*

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

Continuation of Stat. 614 CCH: (1-0)1. Prerequisite: Consent of instructor.

**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. CCH: (1-0)1. *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. CCH: (1-0)1. *Prerequisite: Consent of instructor.*

**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. *Prerequisite: Consent of instructor.*

**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 642 Seminar in Statistics (Non-credit)**

**Seminar course for Ph.D. students in Statistics**

**STAT 699 Ph.D. Thesis in Statistics (Non-credit)**

**STAT 800-899 Special Studies (4-2)Non-credit**

**STAT 900-999 Special Topics (4-0)Non-credit **