Athens University of Economics and Business-Department 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:

  1. The first semester includes 4 compulsory courses (total of 30 ECTS)
  2. In the second semester, each student chooses 2 out of 3 available course groups and attends 8 courses (total of 30 ECTS). These three course groups are: Applied Statistics (A), Computational Statistics (B) and Stochastics (C).
  3. Each course group consists of 4 courses. Each groups 4th course is described in a general manner, as it is a free course open to changes each academic year.

 

 

 

 

 

 

 

PROGRAM STRUCTURE

Semester

’ Semester

Compulsory

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)

 

 

 

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 students 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 re-examined 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 thesiss subject from a topic list posted on the Departments 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 re-take 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.

 

Courses Content

 

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.

 

 

 

Semester

 

Group 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 time-series and partial autocorrelation function. AR, and ARMA models. Wolds 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. Non-parametric methods: Kaplan-Meier, Greenwood formula, Nelson-Aalen estimator; Graphical methods for goodness of fit. Cox Regression, non-proportional 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, Two-phase-sampling, Dual-frame sampling, Domain estimation, small-area estimation, Variance estimation in complex surveys (linearization, replication methods), Non-sampling errors:  Non-response 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. Age-specific rates and probabilities of vital events. Exposed-to-risk 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, k-nn, 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, 3-way 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.

Mean-Variance 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, Out-of-sample forecasting performance, Empirical application. Heteroskedasticity Models, Characteristics of financial returns, ARCH, GARCH and EGARCH models, Properties of time-varying 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 non-conforming (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, -algebra 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 Radon-Nikodym Theorem, Central Limit theorem.

 

Advanced Stochastic Processes

Discrete and continuous Martingales. Markov property. Poisson process. Brown movement. Introduction to Itos 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. Black-Scholes 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.