Curriculum

Prior to enrolment, candidate chooses a supervisor and one of seven modules. In cooperation with the supervisor, the candidate selects courses from the list of obligatory and elective courses. Each student must complete four obligatory core courses. In the 1st year of study, courses New Developments in Statistics (5 ECTS), Statistical research (5 ECTS) and Methodology of Statistical Research (5 ECTS) are obligatory for all students. In the 2nd year of study, students select another obligatory course from the courses in the Selected Topics (on the respective module).

Candidates also choose 3 elective courses worth 5 ECTS from the list of elective courses. They can select 10 ECTS from elective courses from other doctoral programmes at the University of Ljubljana and comparable programmes of foreign universities. The selected courses must be approved by the mentor and the module coordinator.

In the first year of study, doctoral students obtain 15 ECTS from three obligatory courses: New Developments in Statistics, Statistical research and Methodology of Statistical Research. They also choose three elective courses (15 ECTS in total) according to the field of research.

In the second year of study, students choose an obligatory module course (Selected Topics on the respective module) and present their doctoral dissertation topic at the end of the 1st semester.

The core of the third and fourth year is research work for the doctoral dissertation and preparation of the doctoral dissertation.

In the fourth year of study, doctoral students present the doctoral dissertation before the public defence and defend it publicly.

Research work is completed when the student publishes at least one scientific article with the student's name listed as first author. The scientific article must be published or accepted for publication in an internationally recognised scientific journal relating to individual scientific disciplines (SCI or SSCI) before the student hands in the doctoral dissertation for assessment.

In the first year, students must complete three obligatory core courses: New Developments in Statistics, Statistical Research and Methodology of Statistical Research. In the second year, students select another obligatory course from the courses in Selected Topics (on the relevant module).

This course is obligatory for students of all modules.

Applications of statistics are based on a collection of fundamental ideas. The purpose of the course is to systematically present the fundamental chapters of statistics with emphasis on the theoretical basis for various applications. The acquired knowledge is a starting point for independent work in statistics.

Contents will be selected among the following topics:

• Overview of probability.

• Sampling, sampling distribution, standard error, confidence intervals.

• Statistical models, formulation of models, parameters, examples of models, the significance of models for data analysis, forecasting, limitations of statistical models.

• Parameter estimation. Methods for parameter estimation, standard errors, asymptotic properties of estimators, optimality.

• Hypothesis testing, test statistics and their distributions, likelihood ratio test, asymptotic properties of tests, Neyman’Person lemma, optimal tests, analysis of variance.

• Linear regression, assumptions of linear regression, least squares method, Gauss-Markov theorem, forecasting, general linear hypothesis, diagnostic methods, generalizations of regression models.

• Nonparametric methods, nonparametric hypothesis tests, Comparison to classical hypothesis tests.

• Models of time series, ARIMA models, parameter estimates, hypothesis tests.

• Simulation, random number generation, generation of a given distribution, bootstrap, jack-knife, limitations of simulations

This course is obligatory for students of all modules.

The aim of the course is to give an overview of the most contemporary and fundamental fields of statistics and to put the students in contacts with the experts in these fields. Lectures will be given by local and foreign experts in each selected field.

Contents will be selected among the following topics:

• Mathematical statistics.
• Bayesian methods in statistics.
• Simulation methods for statistical research.
• Point processes.
• Time series.
• Multivariate analysis.
• Analysis of nominal data.
• Statistical modelling.
• Nonparametric statistics.
• Research design and data collection.
• Measurement and data collection in official statistics.
• Survey methodology.
• Missing data.
• Network analysis.
• Event history analysis.
• Methods for analysing high-dimensional data.
• Design and analysis of experiments.
• Psychometrics.
• Data mining methods.
• Statistical process control.
• Specific statistical approaches and methods in biology, social sciences, economics and management, medicine, psychology, engineering and other sciences.

This course is obligatory for students of all modules.

Under the guidance of their supervisor, the student conducts one or more statistical analyses for specific clients. The student may participate in all stages of the research and gain insight into the work of a statistician within a research team.

The student also prepares a seminar paper and a presentation on a selected statistical topic and attends presentations given by other students.

This course is obligatory for students enrolled in the Biostatistics module.

Students choose one of the following three subjects:

1. Survival analysis

• Basics:

  • Censoring, survival curve, hazard function

  • Regression models in survival analysis

  • Counting processes

• Specific methods and chapters

  • Goodness of fit

  • Explained variation

  • Relative survival

  • Linear model for censored data

  • Pseudo-observations

  • Competing risks and multistate models

2. Methods for analysing highdimensional data with applications in bioinformatics:

• Basics:

  • Statistical properties of highdimensional data

  • Highdimensional data in biomedical research

  • Methods for multiple testing and classification

• Specific methods and chapters:

  • Types of errors in multiple testing

  • Adapted and non-adapted p-values and the control of type I error

  • Multivariate permuation methods

  • Multivariate classification functions

  • Estimation of predictive accuracy

3. Design and analysis of experiments

• Basics:

  • Overview of the basic ideas (vsebinsko pomembni pojmi)

  • Basics of experimental design: properties, usage, advantages and disadvantages

  • More complex experimental designs: properties, usage, advantages and disadvantages

  • Statistical analysis: parametric and nonparametric approaches

  • Generalized linear models and their application in the analysis of experiments

• Specific methods and chapters:

  • Modelling: various approaches and their usage

  • Response surfaces

This course is obligatory for students enrolled in the Statistics for Social Sciences module.

Data collection:

• Survey data collection in social sciences.

• Secondary sources, administrative data, technical data collection and observational method.

• The role of new technologies.

• Data quality and optimization of costs.

• Processing, archiving and comparative research.

• Ethical and professional standards.

Statistical analysis:

• Introductory overview of approaches and models.

• Multivariate analysis of variables based on nominal, ordinal, interval and ratio scales.

• Exploratory data analysis and data mining.

• Missing data treatments:
  classical approaches (deletion, weighting, single value imputations) and modern approaches (FIML, EM algorithm, multiple imputations).

This course is obligatory for students enrolled in the Economic and Official Statistics module.

Contents will be selected among the following topics depending on the topic of the doctoral dissertation:

• Statistical systems in economics and business sciences.
• Statistical consulting.
• National accounts and transfers across generations.
• Index numbers and composite indicators.
• Demographic analysis and models.
• Data processing in official statistics.
• Data collection in official statistics.
• General regression model, estimators, asymptotic analysis and statistical inference.
• Discrete choice, time series, panel data and multivariate models.
• Multilevel regression models.
• Network Analysis in Economics.
• Other relevant and current topics.

This course is obligatory for students enrolled in the Business Statistics module.

Contents will be selected among the following topics depending on the topic of the doctoral dissertation:

• Statistical systems in economics and business sciences.
• Statistical consulting.
• Index numbers and composite indicators.
• Customer data analysis.
• Statistical quality control.
• Categorical data analysis.
• Multilevel regression models.
• Network analysis in business.
• General regression model, estimators, asymptotic analysis and statistical inference
• Discrete choice, time series, panel data and multivariate models.
• Business process modeling.
• Qualitative research for business.
• Other relevant and current topics.

This course is obligatory for students enrolled in the Mathematical Statistics module.

Basics of mathematical statistics:

• Core topics: Order Statistics. Sufficiency, completeness and unbiasedness. Point estimation. Testing hypotheses. Sequential procedures. Confidence regions. Tolerance intervals. Least square estimators.Analysis of variance.

Bayesian methods in statistics:

• Core topics: Single-parameter models, multi-parameter models and connections to standard statistical methods. Hierarchical models. Model checking and sensitivity analysis. Study design in Bayesian analysis. Introduction to regression models.

• Optional topics: Approximation based on posterior models. Posterior simulation. Markov chain simulation. Other specific models of Bayesian data analysis.

Mathematical methods in econometrics:

• Core topics: Linear and nonlinear regression. Heteroskedasticity and autocorrelation.

Stochastic processes:

• Coretopics: Markov chains. Renewalprocesses. Pointprocesses. Continuous time Markov chains. Brownianmotion.

This course is obligatory for students enrolled in the Psychological Statistics module.

1. Research design and data analysis:

• research designs in psychology and psychometrics, and their epistemological aspects;

• computer simulation;

• the use of large databases;

• programming in a selected language (R, Matlab etc);

• specific aspects of reporting the research outcomes in the area of psychological statistics.

2. Selected topics in psychometrics:

• special topics in classical test theory (lower bounds to the reliability, bounding the true score, generalizability theory);

• conceptual problems of psychological measurement (the validity problem, measurement scales, the nature of latent variables);

• facet theory;

• unfolding and preference scaling;

• comparative evaluation of psychometric paradigms.

3. Analysis of group differences:

• a review of multifactorial designs;

• resampling and robust methods;

• (multivariate) analysis of (co)variance, repeated measures analysis;

• grafical analysis, contrasts, post-hoc tests;

• linear mixed models.

4. Modeling in psychology:

• the general linear model and its properties;

• optimization methods in multivariate analysis;

• hierarchical linear models;

• latent variables and advanced topics in factor analysis;

• structural equation modeling: path analysis, confirmatory factor analysis, general structural model; interaction, moderation and mediaton; modelling of growth and change;

• preference and nonmetric data analysis; categorical data analysis.

This course is obligatory for students enrolled in the Technical Statistics module.

Statistical methods in technical engineering and industry (different types of production systems and use of statistical methods for problem solving in these systems; different types of using statistical methods in technical engineering). Sampling plans for product inspection (determination of the sampling plan, different types of sampling, international standards). Methods of statical process control (basic concepts of control charts, tests of randomness, advanced methods of process tracking).

Design and analysis of experiments (blocking and randomization, incomplete block designs, factorial experiments). Quality by product and process design (determination of design parameters, Taguchi’s methods, product optimization using loss function, tolerance design). Reliability analysis (basic notions, estimation of reliability).

Candidates can choose between 30 elective courses worth 5 ECTS from the list below. They can select 10 ECTS from elective courses from other doctoral programmes at the University of Ljubljana and comparable programmes of other universities.

The selected courses must be approved by the supervisor and the module coordinator. 

Students of the module Mathematical Statistics choose one course from the list of elective courses in the Interdisciplinary Doctoral Programme in Statistics, whereby they cannot choose courses for non-mathematicians (marked by * on the list) and two elective courses offered at the Doctoral Degree Programme Mathematics and Physics at the Faculty of Mathematics and Physics, Department of Mathematics.

• Simple correspondence analysis.
• Multiple correspondence analysis.
• Logistic regression (including methods for repeated measurements).
• Log-linear models.

1. Introduction to customer data analysis.

2. Customer life cycle and typologies of customer data.

3. Data sources for customer data analysis.

4. Databases and data warehouses of customer data.

5. Customer equity and customer lifetime value measurement

6. Customer profiling:

• RFM technique.

• Factor analysis.

• Cluster analysis.

7. Customer response modelling:

• Regression.

• Decision trees.

• Neural networks.

8. Market basket analysis.

9. Special topics in customer data analysis:

• Data mining and customer data analysis.

• Web mining and customer data analysis.

• Dealing with nominal data.

• Dealing with large datasets.

• Dealing with unbalanced datasets.

The course will be centred about the selected topics from the following research areas:

- data pre-processing, outlier detection, feature construction, discretization,

- feature subset selection,

- explorative data analysis, visualization, intelligent visualization techniques,

- predictive modelling (classification and regression) with emphasis on representative and state of the art techniques (Bayesian modelling, support vector machines, rule-based modelling),

- fundamentals of clustering techniques (hierarchical, k-means),

- association analysis,

- model evaluation and scoring,

- industrial, scientific, and business applications of data mining, fundamentals of text and web-mining,

- data mining tools, with emphasis on script-based approaches and visual programming frameworks.

• Modern approaches in survey methodology.

• Administrative sources and registers.

• Big data.

• Integration of multiple data sources.

• Other current issues of data collection in official statistics, e.g. response burden, automated data capture etc.

Data processing, protection and dissemination in official statistics:

• Methods and techniques of data editing, weighting, imputation and variance estimation.

• Data editing for time series analysis, preliminary estimates and revisions.

• Small area estimation.

• Statistical disclosure control and data confidentiality.

• Data description and visualisation, data mining and knowledge creation.

I. Demographic analysis

1. Longitudinal and cross-section analysis

2. Demographic processes: nuptiality, fertility, mortality and migration

3. Population growth and generations replacement

4. Population projections

5. General population development

6. Population policy and population economics

7. Population policy-relevant Principles of New Economy

II. Demographic models

8. Population dynamics models

9. Economic demographic models

10. Other demographic models

11. Demographic pressure on sustainability of the pension and health system in the future.

12. The use of demographic software

• Basic concepts.

• Simple experimental designs: characteristics, impementation, adventages and disadvantages.

• Compex experimental designs: characteristics, impementation, adventages and disadvantages.

• Statistical analysis: parametric and non parametric approach.

• Generalized linear models and their application for analysis of experiments.

1. Introduction to environmental statistics.
2. Spatial statistics.
3. Nonstationary spatial models.
4. Models defined by conditional distributions.
5. Design of monitoring networks.
6. Spatial-temporal statistics.
7. Trends in environmental time series.
8. Extreme values.

1. Theory of cost of living index.

2. Theory of index numbers in time series.

3. Elementary indices and index aggregation in several stages.

4. Productivity measurement.

5. Decomposition of index numbers.

6. Hedonic indices.

7. Indices in practice and issues of reliability.

8. Construction of composite indicators.

a) pros and cons

b) steps for construction

c) a quality framework for composite indicators

9. Toolbox for constructors.

10. Composite indicators in practice:

a) New Economy indicators

b) key performance indicators

Internet research:

• Concepts of Internet mediated research.
• Reactive and non-reactive data collection methods.
• Ethical issues in internet mediated research.

Web surveys:

• Typology of web surveys.
• Software tools for web surveys.
• Probability and nonprobability samples in web surveys.
• Statistical inference on the basis of nonprobability samples.
• Web survey errors (sampling frame, measurement, nonresponse…).
• Web questionnaire design for various devices.
• Mixed-mode surveys.

Selected topics in Internet research:

• Technical measurement (log files, paradata, measuring movement and location …) and big data.
• Introduction to online qualitative methods.
• Combining web-based quantitative and qualitative methods (mixed-methods).
• Human-computer interaction and web-based data collection.

Vector spaces

• Eigenvalues and eigenvectors

• Generalized inverses

• Systems of linear equations

  Optional material:

• Matrix factorizations and matrix norms

• Partitioned matrices

• Matrix derivatives

• Quadratic forms

Order Statistics.

Sufficiency and completeness.

Point estimation.

Hypothesis testing.

Sequential procedures.

Confidence regions.

Least square estimators.

Analysis of variance.

Nonparametric inference.

Introduction to Bayesian Statistics.

1. Empirical regression and the algebra of least squares.

2. The classical linear regression model and its generalization.

3. The likelihood function, statistical distributions and testing principles.

4. Asymptotic analysis: Stochastic convergence and asymptotic properties of estimators.

5. Estimation and testing in the generalized regression model.

1. Generalized linear regression models.

2. Time series models.

3. Discrete choice models and limited dependent variable models.

4. Panel data models.

5. Nonlinear regression and multivariate models.

1. Classical test theory:

- test score, true score and error;

- models and methods for reliability assessment ;

- practical uses of the reliability coefficient in test construction and score interpretation;

- reliability and the latent structure of a test.

2. Item response theory:

- fundamental measurement and the Rasch model;

- checking the model assumptions;

- other logistic models (for binary, ordered response and categorical items);

- multidimensional models; item factor analysis;

- test construction and adaptive testing;

- parallel forms construction and identification of DIF.

3. A review of other paradigms of the behavioural response measurement.

1. The idea of multilevel modelling

• Sources of clustered data
• Multilevel Theories

2. Two level models

• Linear random intercept model
• Linear random slopes model

3. Three level variance component model

4. Cross level coefficients

5. Logistic random coeficient models

6. Logistic three level models

• Graphical representations of multivariate data
• Multiple regression
• Cluster analysis
• Principal component analysis
• Factor analysis
• Structural equation modeling
• Other methods based on available time:
  • Canonical correlation analysis
  • Discriminant analysis
  • Multidimensional scaling
  • Corespondence analysis
• Overview of some other multivariate methods

• Consistency between the systems of macroeconomic statistics and international comparability of economic aggregates,

• Satellite accounts of different areas of economic policy,

• Social accounting matrices (SAM) as statistical basis of models,

• Introducing age dimension into the system of national accounts,

• Transfers across generations,

• Unpaid household work by age: production, consumption and transfers,

• Population ageing and generational economy.

• Introduction, basic notions.
• Sources of networks and collection of network data.
• Quality of network measurement.
• Types and representations of networks, network analysis software.
• Structure of networks: connectivities, partitions, components, cuts, cores, reductions, pattern search.
• Measures of centrality and importance, islands.
• Valued networks, Markov chains as networks.
• Acyclic networks.
• Two-mode networks and multiplication of networks.
• Temporal networks.
• Clustering and blockmodeling.
• Statistical analysis and modeling of networks; scale free networks.
• Use of network analysis: genealogies, internet, text analysis, scientometrics,  etc.

1. Introduction to network analysis.

2. Interorganizational networks.

2.1 Interorganizational networks typology.

2.2 Data sources and data collection for interorganizational networks.

2.3 Interorganizational networks data analysis.

 3. Intraorganizational networks.

3.1 Types of networks: collaboration, knowledge flow...

3.2 Data sources and data collection for intraorganizational networks.

3.3 Network data collection through questionaires.

Reliability concepts and reliability data (reliability function, failure rate, repair rate, censoring, repairable systems, nonrepairable units, etc.).

Lifetime distribution models. Parametric models (Exponential, Weibull, Extreme Value, Lognormal, Gamma, Birnbaum-Saunders, etc.).

Repair rate models for repairable systems (homogeneous Poisson process, non-homogeneous Poisson processes).

Failure rates models (competing risk model, series model, the parallel or redundant model, r out of n model, standby model).

Choosing life distribution model, testing model assumptions, estimating parameters (Kaplan-Meier product limit procedure, likelihood ratio tests, maximum likelihood estimations etc.).

Graphical methods (probability plotting of complete data, of single censored data, and of multiply censored data).

Bayesian methods used in reliability (prior and posterior distribution models).

Acceleration test models and life tests (Arrhenius, Eyring, etc.).

Introduction to qualitative research: its placement in the research process in comparison with quantitative research, purpose and meaning.

Data sources for qualitative research.

Ethical dilemmas in the process of qualitative research.

Typologies of qualitative research methods.

Questioning-based qualitative research methods.

Observation-based qualitative research methods.

Sampling for qualitative research.

Analytical software support for qualitative research.

Qualitative research in practice.

Other emerging topics.

Computer tools for microarray analysis (R, Bioconductor) and links to data bases and ontologies.

• Plan of experiment.
• Data preparation and preprocessing.
• Background correction.
• Normalization.
• Analysis of differential expression.
• Methods for discovery of related gene sets.
• Graphical data visualization.

• Advanced use of programming environment R.
• Computer oriented approach to statistical methods.
• Robust methods and EDA.
• Random number generators.
• Statistical simulation (Monte Carlo).
• Bootstrap and jacknife.
• Nonparametric estimation.
• Rejection sampling.
• One and multidimensional smoothing.
• Graphical presentation and visualization.
• Reproducible research and reports.

The course introduces relevant methodological and statistical topics from the perspective of statistical consulting, from the perspective of the associated implementations via supporting software, and from the perspective of reporting the results to quantitatively-literate and non-literate audience.

1. Introduction to statistical quality control.

2. Data sources for statistical quality control.

3. Sampling for statistical quality control.

4. Statistical process control

5. Control charts in theory and practice.

6. Experimental research and statistical quality control.

7. Statistical quality control in the service sector.

8. Statistical quality control in real time.

Importance and specifics of data in economics and business sciences.

Measurement in economics and business sciences.

• Concepts and their operationalization.

• Statistical standards.

• Data quality.

Data sources in economics and business sciences.

1. Stochastic processes.

- What is a stochastic process?

- How to describe a stochastic process?

2. Markov chains.

- Discrete time Markov chains.

- Classification of states.

- Strong Markov property.

- Stationary distributions.

- Ergodic properties of Markov chains.

- Monte Carlo simulation.

- Continuous time Markov chains.

- Continuous time Markov chains: examples of application.

3. Time series.

- Examples of time series.

- Stationary time series.

- Autocorrelation and partial autocorrelation.

- ARIMA models.

- Parameter estimation in ARIMA models.

- Kalman filter.

• Survey process and its phases (conceptualization, sampling, questionnaire…).

• Quality of data/processes and related concepts (e.g. TQM).

• Survey costs, errors, management and related concepts (e.g. TSE).

• Sampling and nonsampling errors (i.e. nonresponse, measurement, frame,…).

• Specifics of a survey process in academic, business and private sectors.

• Survey modes (personal, telephone, mail, web surveys…).

• Questionnaire design.

• Measurement, validity, reliability.

• Editing, coding, documenting, processing and archiving.

• Missing data:

  • classical approaches (ignoring, weighting, imputation) and

  • modeling approaches (ML, EM algorithm, Bayesian approach, MI).

• Data linking, statistical matching and data fusion.

• Introduction to data modeling.

• Guidelines, recommendations and professional standards (e.g. TDM).

• The concept of e-Social Sciences.

Statistical methods for solving problems in technical engineering:

Experimental design and sampling. Data presentation. Hypothesis tests. Regression and correlation. Analysis of experiments. Time series. Sampling plans and methods of statistical process control. Usage of statistical software packages for solving statistical problems in technical engineering.