Athens University of Economics and BusinessDepartment of Statistics
Full time Master in Statistics
Program Aims
The program aims to provide education to graduates from many scientific areas to statistical science and its applications. Successful graduates should, at the end of their studies, be able to use statistics for solving quantitative problems in a variety of scientific fields.
To fulfill these objectives, offered courses cover a large spectrum of contemporary statistical theory, methodology and its applications, with particular emphasis on modern computational techniques. At the same time, given the fact that statistics often aim at applications in other scientific areas, specialized courses are offered regarding statistical methodology with applications in: social sciences, economics, finance, medicine, environment and industry.
Graduates can work in statistical research companies, research institutes, consulting firms, banks and the public sector.
Applicants can be graduates of majors in Statistics, Mathematics, Polytechnic Schools, Economics or other related fields.
Duration of the program
The duration of the taught courses is 2 semesters. After the successful examination of all courses, students are required to write a thesis. It is common that the completion of the thesis require not more than six months.
Course structure
To obtain a Masters in Statistics in the full time program, students must attend and successfully pass the exams in fourteen courses distributed in two semesters.
The structure of the program is formed as follows:
PROGRAM STRUCTURE 

Á’ Semester 
Â’ Semester 
Compulsory 
Á Group  Applied Statistics 
Probability for Statistics (7,5 ECTS  36 hours) 
Time Series Analysis (4 ECTS  18 hours) 
Computational Statistics (7,5 ECTS  36 hours) 
Biostatistics (4 ECTS  18 hours) 
Generalized Linear Models (7,5 ECTS  36 hours) 
Advanced Methods in Survey Sampling (3,5 ECTS  18 hours) 
Data Analysis (7,5 ECTS  36 hours) 
Advanced Models (3,5 ECTS  18 hours) 



Â Group  Computational Statistics 

Statistical Learning (4 ECTS  18 hours) 

Bayesian Models in Statistics (4 ECTS  18 hours) 

Financial Econometrics (3,5 ECTS  18 hours) 

Topics in Statistics (3,5 ECTS  18 hours) 



C Group  Stochastics 

Probability Theory (4 ECTS  18 hours) 

Advanced Stochastic Processes (4 ECTS  18 hours) 

Stochastic Models in Finance (3,5 ECTS  18 hours) 

Topics in Stochastics (3,5 ECTS  18 hours) 


After successful completion of the courses, each student must prepare and submit a thesis on a topic, under the guidance of a supervisor.
Regarding the thesis, students should have in mind that:
1. Each student’s thesis is presented in the form of a (relatively) short presentation. The examination committee consists of three examiners, one of which is the corresponding supervisor. Thesis presentation can take place either in February, June or October, at a predefined date. In case the examination committee rules the dissertation to be unsatisfactory, the student has the right to be reexamined only once more. If the student fails again, he is entitled to a certificate indicating the courses he has successfully completed.
2. Each student can choose the thesis’s subject from a topic list posted on the Department’s website until the end of April. Final thesis assignment is done exclusively from this topic list.
Cost
The tuition fees for the full time Master Program amounts to 3,000 Euros. A number of scholarships are available. Students admitted to the full time program whose undergraduate total degree is more than 8 are entitled to a reduction of 1/3 of the total tuition fees. Partial or complete exemption from tuition fees can also be granted to students with outstanding performance during their studies, on the recommendation of the corresponding supervisor, the program director and the approval of the Departments Committee.
Terms of studies
Teaching and examinations are all conducted in English, unless all participants are Greek speakers. In this case, courses can be in Greek too. Attendance of lectures is compulsory and absence in 25% or more of the lectures is an objective reason of failure in examinations of the corresponding course.
Examinations are conducted at the end of each semester. There is no limit to the number of allowed failed courses (both at the regular and the follow up exams). However, students have the right to retake the examinations once more until next September. If a student fails to pass a course even after that period, he is entitled a certificate indicating the courses he has successfully completed. A Postgraduate Committee is responsible for all academic aspects of the study.
Á’ Semester
Probability for statistics
Basic probability and probability distributions, introduction to stochastic processes, likelihood, sufficiency, significance tests, hypothesis testing, introduction to Bayesian statistics, elements of asymptotic theory, basic asymptotic results.
Generalized Linear Models
Introduction to modeling through linear equations, exponential family and components of a GLM, binary data, logistic models, contingency tables, loglinear models, Poisson data, normal data, gamma data, normal mixed models, GLMM models.
Computational Statistics
R programming, simulation techniques, numerical methods for stats, MCMC simulation, bootstrap techniques, smoothing.
Data Analysis
Projects on regression, design of experiments, ANOVA models, likelihood fitting, normal longitudinal data, GLM for dependent observations, Bayesian modeling.
Â’ Semester
Group Á – Applied Statistics
Time Series Analysis
First and second order stationarity, autocorrelation function of stationary time series and estimation. Test of independence. Parametric and no parametric components of a time series. The method of differences. Forecasting of stationary timeseries and partial autocorrelation function. AR, and ARMA models. Wold’s decomposition theorem. Estimation of autocovariance functions and partial autocorrelation for ARMA models, asymptotic properties, model choice.
Biostatistics
Basic principles, hazard and survival functions. Parametric methods, likelihood function. Nonparametric methods: KaplanMeier, Greenwood formula, NelsonAalen estimator; Graphical methods for goodness of fit. Cox Regression, nonproportional hazards models (ACF etc). Competing Risks; Random effect models; model selection. Martingales approach in survival.
Advanced Methods in Survey Sampling
Basic theory of sampling from finite populations, Use of auxiliary information in estimation, Calibration and Generalized Regression, Twophasesampling, Dualframe sampling, Domain estimation, smallarea estimation, Variance estimation in complex surveys (linearization, replication methods), Nonsampling errors: Nonresponse and Imputation, Sampling rare populations, indirect sampling, Use of models in survey sampling.
Advanced Models
The Role of Demographic Statistics, Populations: Open and closed, de facto and de jure populations. Sources of Demographic data. Cohort and case control studies. Lexis Diagram, Demographic Measures, Demographic databases. Sampling design and Inference. Agespecific rates and probabilities of vital events. Exposedtorisk populations. Standardization techniques. The life table as a single decrement process. Stochastic investigation of life table functions. Survival function, force of mortality. Multiple decrement processes. Modeling mortality patterns. Parametric and nonparametric modeling. Mortality forecasting techniques. Fertility measures. Modeling fertility patterns. Parametric and nonparametric modeling. Population projections and forecasting techniques. Uncertainty in demographic forecasts: Concepts issues and evidence. Small area estimates and forecasts.
Group B – Computational Statistics
Statistical Learning
Unsupervised learning: association rules, clustering, self organizing maps Supervised Learning: LDA, QDA, knn, penalized LDA Kernel methods and regularization methods (Ridge, Lasso, Elastic Net) Model Assessment and Selection.
Bayesian Models in Statistics
Introduction to basic principles of statistical modeling. Basic principles of Bayesian statistics (conjugate priors, Laplace approximations). MCMC algorithms for the estimation of posterior distributions (Gibbs sampling, Metropolis Hastings, other algorithms). Model specification in WinBUGS. The Deviance Information Criterion (DIC). Some simple examples for Bernoulli, Binomial, 2x2 Contingency Tables, 3way Tables . R2WinBUGS: Running WinBUGS from R. Bayesian analysis of Normal linear models. Bayesian ANOVA and the use of Dummy variables. Bayesian GLM (Poisson and Binomial models). Advanced GLM based models and extensions. General modeling issues: Model parameterizations and identifiability and priors. Introduction to hierarchical Models. Hierarchical models using Examples from WinBUGS. Bayesian model comparison and variable selection.
Financial Econometrics
Introduction to Course: Outline of Topics, Basic Econometric Models.
MeanVariance Portfolio Theory, Return and risk, Portfolio diversification, Construction of optimal portfolios, Basic empirical application. Testing the Capital Asset Pricing Model (CAPM) and Multifactor Models, Market Model, Multifactor models, Multivariate multifactor models, Empirical application. Predicting Asset Returns, Autocorrelations, Alternative predictors and models, Outofsample forecasting performance, Empirical application. Heteroskedasticity Models, Characteristics of financial returns, ARCH, GARCH and EGARCH models, Properties of timevarying models, Estimation of heteroskedastic models, Multivariate (G)ARCH models, Empirical application (portfolio construction). Risk Measures, Value at Risk, Expected Shortfall, Empirical application. Panel Data, Introduction to panel data, Fixed effects model, Random effects model, Empirical application.
Topics in Statistics
Basic concepts: Phase I/II, common/assignable causes of variation, ARL, ATS, Magnificent Seven, Six Sigma methodology. Control charts for variables, OC curve, variable sample size, estimating the parameters. Control charts for attributes: fraction nonconforming (Binomial Case), nonconformities (Poisson case) OC curve, Estimating the parameters. CUSUM and EWMA control charts. SPC for Autocorrelated data, Multivariate SPC, Change Point Methodology, Bayesian SPC, Engineering/Algorithmic Process Control, Acceptance Sampling.
Group C – Stochastics
Probability Theory
Probability Space, óalgebra and probability measures. Borel Cantelli. Random variables as measurable functions. Average and the Lebesque integral. Random variables convergence notions: with probability1, by probability, in L^p and by distribution. Strong and weak laws fo large numbers. Conditional mean and conditional probabilities – RadonNikodym Theorem, Central Limit theorem.
Advanced Stochastic Processes
Discrete and continuous Martingales. Markov property. Poisson process. Brown movement. Introduction to Ito’s theory of integration. Stochastic differential equations.
Stochastic Models in Finance
Options pricing in the binomial model. Martingales. Stochastic Differential Equations. Change of measure and the Cameron Martin Girsanov theorem. Self financing portfolios. BlackScholes model. Pricing market securities. Interest rate models.
Topics in Stochastics
Introduction to Stochastic Epidemic Modeling, Stochastic versus deterministic models. Stochastic epidemics in large communities. The Sellke construction, The Markovian case, Exact results. Coupling methods. Examples, Definition of coupling, Applications to epidemics. The threshold limit theorem, The imbedded process, Convergence results, Duration of the Markovian SIR epidemic. Density dependent jump Markov processes. Multitype epidemics. Household model. Epidemics and graphs, Random graph interpretation, Epidemics and social networks. Disease Control. Estimating vaccination policy, Estimation of vaccine efficacy.