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Master of Science in Statistics

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Hakkında yorumlar Master of Science in Statistics - Kurumda - Çankaya - Ankara

  • Program tanımları
    MASTER OF SCIENCE CURRICULUM IN STATISTICS  

    M.S. PROGRAM      

    Statistics Option       
    STAT 500 M.S. Thesis   
    STAT 501 Statistical Theory I     
    STAT 502 Statistical Theory II     
    STAT 542 Seminar in Statistics     

    Three electives from Modeling, Computing or Elective Course list

    Two electives from any of the following course groups or out of department   

    Totally seven courses with at least 21 credit hours        


    Interdisciplinary Statistics Option for non-majors       

    STAT 500 M.S. Thesis
    STAT 551 Probability and Statistics I    
    STAT 552 Probability and Statistics II     
    STAT 542 Seminar in Statistics         

    One Computing course

    One Modeling course

    One Elective course       

    Two electives from any of the following course groups or out of department   

    Totally seven courses with at least 21 credit hours        


    Computing Courses
    STAT 554 Computational Statistics (*)
    STAT 555 Advanced Computational Statistics
    STAT 556 Advanced Computing Methods in Statistics  

    Modeling Courses      
    STAT 503 Linear Statistical Models
    STAT 525 Regression Theory and Methods
    STAT 557 Statistical Modeling I (*)     
    STAT 558 Statistical Modeling II (*)
    STAT 559 Applied Multivariate Analysis    
    STAT 560 Logistic Regression Analysis    
    STAT 561 Panel Data Analysis     
    STAT 562 Univariate Time Series Analysis
    STAT 563 Multivariate Time Series Analysis  

    Elective Courses
    STAT 504 Non-Parametric Statistical Inference and Methods
    STAT 505 Sampling Theory and Methods
    STAT 509 Applied Stochastic Processes
    STAT 518 Statistical Analysis of Designed Experiments
    STAT 553 Actuarial Analysis and Risk Theory
    STAT 564 Advanced Statistical Data Analysis
    STAT 565 Decision Theory and Bayesian Analysis
    STAT 566 Reliability Theory and Methods
    STAT 567 Biostatistics and Statistical Genetics
    STAT 568 Statistical Consulting  

    (*) Starred courses can only be taken by the students of Interdisciplinary Statistics Option

    DESCRIPTION OF COURSES

    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)

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