Graduate Courses

810501 Probability Theory (3,0,0) 3: Measure and probability spaces, product spaces, extension theorem, measurable functions and random variables, expectation, characteristic functions, independence, convergence.

810502 Statistical Theory (3,0,0) 3: Sample Statistics and sampling distributions, parameter estimation and methods, small and large sample properties of estimators, hypothesis testing, Neyman-Pearson Lemma, monotone likelihood ratios, similar tests and likelihood ratio tests.

810503 Multivariate Statistics (3,0,0) 3: Vector spaces, random vectors, multivariate normal distribution, estimation of mean vector and covariance matrix, inference for mean vectors and covariance matrices, likelihood ratio tests, t statistics, comparison of mean vectors, MANOVA.

810504 Multivariate Modeling and Analysis (3,0,0) 3: Multivariate linear regression models, canonical correlation, analysis of covariance structure, principal components, factor analysis, classification and clustering techniques.

810505 Optimization (3,0,0) 3: Convex analysis, primal and dual formulation of problems, linear and non-linear programming, quadratic programming, separable programming, convex programming, genetic algorithms, applications.

810506 Operations Research Methods (3,0,0) 3: Models and principles of modeling in operation research; scientific method,. network analysis, queuing and inventory models, advanced topics in linear programming, dynamic programming, non-linear programming, decision analysis.

810507 Measure Theory (3,0,0) 3: General measures, external measure and measure and extensions, measures in several spaces, measurable functions, ıntegrals and integration by measures, probability measure, random variables and expectation, convergence in distribution, derivation; conditional probability; martingales, measure theory for stochastic processes and applications.

810508 Introduction to Stochastic Processes (3,0,0) 3: Mathematical foundations of stochastic processes, trajectories, classification of processes, stationary, normal processes and covariance stationary processes, counting processes, renewal processes, Markov processes.

810509 Statistical Computing (3,0,0) 3: Computer organizations, errors in computing, programming and statistical, software, probability distributions and their numerical calculations, selected computational methods for linear algebra and matrices, computing subjects in statistical analysis; linear models, experimental design, unconstrained optimization, nonlinear models, multivariate methods.

810510 Statistical Quality Control (3,0,0) 3: Process control, control charts, special process control methods, acceptance sampling; quality control by attributes and variable based sampling, life tests and reliability analysis.

810511 Statistical Decision Theory (3,0,0) 3: Subjective probability and utility, Bayes risk and Bayes decision, prior, posterior, conjugate prior distributions and asymptotically versions, sequential decisions and optimal stopping.

810512 Data Analysis and Interpretation (3,0,0) 3: Presentation of data by useful graphics and displays, boxplots and batch comparisons, mathematical aspects of data transformations, resistant lines, median polish for two or more ways tables, error analysis, refined estimators, L-,M-,W- estimators, robust location, scale and range estimators.

810513 Linear Models (3,0,0) 3: Linear and quadratic forms, expectation operations for matrices and their functions, distribution of quadratic forms, general linear hypothesis and least squares theory, full and less than full rank models, design models variance components models, estimation, hypothesis testing and correlation analysis, anova and regression, tolerans intervals, simultaneous inference, multiple comparisons.

810514 Statistical Design of Experiments (3,0,0) 3: Randomization and blocking rules, balanced and unbalanced, complete and incomplete blocks designs, factorials design, mixed designs, optimal allocation of observations, general analysis and statistical inference.

810515 Time Series Analysis (3,0,0) 3: Random fields, autocovariance and autocorrelation functions, trends, seasonally and smoothing, fourier analysis, spectral theory, large sample theory; convergence in distribution, estimation of expectation functions, periodogram, estimation of spectrum, filtering, transformations, arıma models, other modeling approaches and statistical analysis.

810516 Sampling (3,0,0) 3: Randomization theory for simple and multi-stage sampling. Sampling with and without replacement. Proportional and disproportional sampling. Ratio and regression estimates. Stratification; clustering; systematic sampling; double sampling and related problems.

810517 Advanced Probability Theory (3,0,0) 3: Probability spaces, Lebesgue integral, Radon-Nikodym theorem, characteristic function, convergence, limit theorems, stable distributions, infinity divisible distributions, ergodic theorems, martingales.

810518 Advanced Statistical Theory (3,0,0) 3: Measure and integration, statistical inference and decision, determination of the decision problems, Bayes and minimax methods, maximum likelihood, complete classes and sufficient statistics, exponential families, uniformly most powerful tests, unbiasedness and invariance, linear hypothesis, sequential ratio tests.

810519 Multivariate Statistical Inference (3,0,0) 3: Inner product spaces, outer product, random vectors, normal distribution, jacobians, exterior product, invariance of measures, Wishart, T, Beta, U distributions; tests for mean vector and covariance matrix, general linear hypotheses, tests for correlation coefficient, canonical correlation, multivariate data analysis.

810520 Discrete Multivariate Statistical Analysis (3,0,0) 3: Some discrete multivariate distributions, sampling models, asymptotic methods, structural models, maximum likelihood estimates for contingency tables, formal goodness of fit, Markov models, square tables, model selection, measures of association and agreement, pseudo-Bayes estimates of cell probabilities.

810521 Nonparametrical Statistical Inference (3,0,0) 3: Robust statistical inference, inference on and testing hypotheses of randomness, nonparametrical model fitting, tolerance limits; discriminant variance analysis.

810522 Statistical Systems Analysis and Control (3,0,0) 3: Systems definition and classifications, systems analysis by deterministic and probabilistic models, uncertainty component, systems modeling with random inputs, block diagrams and flow diagrams, discrete-time systems, continuos time dynamic systems, transformation, feedback control systems, systems simulation; systems analysis by stochastic modeling.

810523 Spatial Statistics (3,0,0) 3: Spatial processes. heterogeneity, homogeneity and isotropy. spatial random functions. expectation functions; spatial autocorrelation and variogram. Distribution theory for spatial statistics. Regular and irregular point, lattice and grid patterns. pattern recognition and analysis. Parametric spatial models. kriging. Estimation and testing.

810524 Risk Theory and Methods (3,0,0) 3: Definition of risk for systems and processes; quantification of risk, stochastic basis of risk analysis, special functions, model building and analysis; discrete and continuous cases, compound processes, risk limits; failure and ruin probability, reliability analysis.

810525 Actuarial Analysis (3,0,0) 3: Stochastic basis of insurance and risk theory, risk analysis for risky business, loss number and loss size processes; simple, mixed and compound models, dynamical analysis of risk processes, ınsurance and reinsurance models; reserve and premium calculations, ruin probability and risk management, several insurance types,

810526 Advanced Topics in Statistical Inference (3,0,0) 3: Hypothesis testing problems in linear and non-linear statistical models. Large sample properties for estimation and testing. Optimal tests. Consistency problems. Asymptotic theory and several forms of asymptotic efficiency. Statistical inference problems in Bayesian, nonparametric and sequential analysis.

810527 Statistical Inference for Stochastic Processes (3,0,0) 3: Special stochastic process models. Large sample theory. Discrete and continuous parameter processes. Optimal asymptotic tests. Martingales. Stochastic differential equations. Parametric, nonparametric, sequential and Bayesian inference problems.

810528 Limit Theorems in Probability Theory (3,0,0) 3: Limit theorems and probability inequalities for sums of independent random variables, convergence on infinitely divisible distributions, central limit theorems with rates of convergence, the weak and strong law of large numbers, the law of the iterated algorithm, strong limit theorems.

810529 Random Operators and Stochastic Equations (3,0,0) 3: General theory of linear random operators, theory of random matrices, stochastic differential equations, operator stochastic equations and their solutions, systems of algebraic equations with random coefficients; applications to Brownian motion, neural networks, multivariate statistics, pattern recognition and stochastic control theory.

810530 Approximation Theory in Statistics (3,0,0) 3: Sequence of random variables and approximation, approximation in central limit theorems, asymptotic representation theory for sample statistics asymptotic theory in parametric inference, U-statistics, differentiable statistical functions, M-, L-, R- estimates, relative efficiency in approximation.

810531 Asymptotic Techniques in Statistics (3,0,0) 3: Basic limiting procedures, asymptotic expansion and related inferencial concepts, Edgewort and allied expansions, multivariate expansions, direct and generating function approaches, asymptotic techniques for discrete distributions, applications in statistical inference.

810532 Robust Statistical Inference (3,0,0) 3: Refined estimators, W-, M- and L- estimators, selection of robust estimators, resistance and robustness of efficiency, robust scale estimators and confidence intervals, robust approaches to hypothesis testing, bootstrapping and jackknifing techniques.

810533 Bayesian Statistics (3,0,0) 3: Bayes theorem and decision problems, prior information and distributions, Bayesian assessments for statistical inference under non-normal assumptions, Bayesian inference methods for means and variances, data transformations, Bayesian models in statistics and multivariate analysis

810534 Statistical Analysis of Extreme Values and Outliers (3,0,0) 3: Origin of outliers, accommodation approaches in estimation and testing, discordance tests, univariate and multivariate outliers and extreme values, outlying and extreme value problems in structured data; outliers and extreme values in time series, directional data and contingency tables, distributions of extreme values, rank order methods.

810535 Statistical Dependence Theory (3,0,0) 3: Dependency in conditional distributions, conditional independence, statistical inference for dependent systems, stochastic monotone dependence, classification of dependences, ordering of dependencies, dependency concepts in the analysis involving discrete variables, mixing sequences and dependence.

810536 Model Based and Complex Sampling Design (3,0,0) 3: Sampling designs for finite populations, unbiased estimation matters for several sampling designs and variance estimation, estimation by using auxiliary information in model based approaches, domain estimates, optimal designs, designs for multi-purpose complex surveys.

810537 Reliability Analysis (3,0,0) 3: Concepts of risk and reliability of systems, failure and hazard rate functions, reliability estimation in parallel and series systems, reliability analysis for incomplete and censored data of type I and II, life tests, graphical and analytical methods.

810538 Spectral Methods for Time Series (3,0,0) 3: Periodical functions, harmonic analysis, spectrum and it’s estimation, Fourier transforms and their properties, periodgram and it’s properties, asymptotic distributions and inference

810539 General Pattern Theory (3,0,0) 3: Statistical pattern recognition and probability function estimates, topological and dynamical structures, parameter optimization, error functions and their properties, pre-processing of data and generalizations, Bayesian procedures, applications with neural networks, applications in image processing and data analysis.

810540 Stochastic Optimization (3,0,0) 3: Stochastic systems and optimization, dynamic programming, stochastic decomposition, network analysis, stochastic linear and nonlinear programming, restricted hierarchical systems, optimization in statistics, choice of best model, hypothesis testing and optimization, best designs and decision criteria for statistical analysis.

810541 Multicriteria Decision Making Methods (3,0,0) 3: Decision support systems, multiobjective simplex method, several methods and algorithms for optimal results and decisions, generalized games procedures, compromise programming, risk analysis, sensitivity analysis, large scale problems and decomposition principles.

810542 Information Theory (3,0,0) 3: Communication processes, measurements of information, accumulation of information, common information, basic theory of Shannon, conditional information, entropy, entropy and probability distributions, maximum entropy principles, information theory and its applications in decision making and statistical inference.

810543 Sequential Analysis (3,0,0) 3: Sequential tests concept, double sampling procedures, sequential probability ratio tests, composite hypothesis, principles and methods of sequential estimation.

810544 Statistical Programming and Databases (3,0,0) 3: Structural programming, planning and procedures of programming, iteration and searching procedures; designing databases that need to be structured by subject matter, time and spatial dimensions in data, design of databases for efficient computing for estimation and testing.

810545 Latent Variable Models(3,0,0)3: Concepts of latent variables and relevant models, Modeling of latent variables in factor analysis and categorical variables analysis, Estimation of goodness-of-fit, Cross validation assessments, Estimation and computational procedures for latent variable models.

810546 Compositional Data Analysis(3,0,0)3: The place and importance of compositional data in statistics, High dimensionality and mixture variation, Covariance structure and covariate composition, Log-ratio analysis, Sub-compositions and partitioning, Irregular compositional data and directional data analysis, Estimation and testing problems.

810547 Mathematical Foundations of Statistics(3,0,0)3: Set theory, Algebraic foundations, Continuity, limit and convergence, Finite and infinite series and seguences, Advanced differentiation and integral calculus, measurement and measure spaces, Functions and special functions in statistics, Approximation of functions, Optimization in statistics, Modeling and analysis applications of other advanced concepts and methods.

810548 Analysis of Record Values (3,0,0)3: Order statistics,outlier and extreme values and record values relations. Distributions and characterization of distributions for record values. Models of distribution and statistical inference for record values. Assessment on the ground of dependency and multi-variate situations. Estimation and testing problems. Sampling analysis by completion of missing and incomplete values.

810549 Statistical Planning and Inference(3,0,0)3: Statistical modelling about observing and relevant planning for physical, human, technological and economic phenomena, Observation and control of systems. Value of information in decision making. Dynamic general equations expressions for stochastic systems. Planning, control and assessment methods. Statistical inference approaches in investigation of integrated systems.

810550 Advanced Optimization in Statistics(3,0,0)3: Advanced methods for error minimization in statistics: MİNMAD, MİNMAXAD, LS,ML and their combinations in modeling and inference.Simplex procedure and duality in estimation and hypothenis testing. Experiments and optimal designs. Optimal strategies in sampling surveys and cencuses. Dicussion of concurrent issues in optimal statistical decisions.

810551 Statistical Methods and Applications(2,2,0)3: Description of data Random event relations and probability laws. Repeated and replicated sampling. Large sample and small sample inferences. Comparison methods. Hierarchical and sequential models. Modeling dependence in many ways. Analysis of continuous and categorical data. ANOVA and MANOVA. Nonparametric and robust methods. Emphasis on best choice of methods in aplications.Applications in demography, biometry,technometrics and other fields. Analysis and interpretation by using package programs.

810552 Fuzzy Theory in Statistics and Optimization(3,0,0)3: Fuzzy sets. Fuzzy decision and operators. Possibility theory. Fuzzy theory for statistical decision making and statistical modeling. Fuzzy mathematical programming. Possibilistic programming. Stochastic possibilistic programming.

810553 Probabilistic Metric Spaces and Copulas (3,0,0)3: Copulas and random varıables. Survival copulas. Sklar’s theorem. Methods for constructing copulas. Dependence. Empirical copulas. Other relevant topics.

810554 Random Numbers and Simulation (3,0,0)3: System, model and simulation concepts. Random number generators. Monte Carlo methods. Simulation of distributions. Simulation for statistical inference. System simulation. Bootstrap and Jacknife methods.Other variance reduction technıques. Genetic and other general algoriıthms.

810555 Survival Models and Statistical Analysis(3,0,0)3: Lifetime distributions and some important survival models. Censoring and statistical modeling. Life tables. Parametric and nonparametric estimation of survival functions. Statistical inference for various lifetime distribution models. Goodness of fit. Multivariate and stochastic process models for survival analysis.

810599 Statistical Consultancy (0,0,3) 1: Defining and identifying statistical problems and model building, data analysis, inference, usage of statistical software, interpretation and report writing, interdisciplinary applications