Curriculum and schedules
Obligatory courses

Contents will be selected among the following topics:

• Mathematical statistics.
• Bayesian methods in statistics.
• Simulation methods for statistical research.
• Point processess.
• 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 experiements.
• 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.

• 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

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).

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

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.

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.

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.

 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.

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).