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Department of Stochastic Informatics

Research Topics

1. Information in statistical experiments and optimal statistical decisions (estimation, testing, classification), with emphasis on maximum entropy, minimum divergence methods, and asymptotic theory.
2. Robust statistical procedures and their applications in various statistical environments, including adaptivity and self-organization. Regression analysis.
3. Statistical inference in random processes and random fields. Applications in stochastic optimization, change-point, optimum investment portfolios, and image and speech processing.

Personnel

International Cooperation

• Augsburg, Germany (Prof. J. Heinrich)
• Aarhus, Denmark (Prof. E.B. Vedel-Jensen)
• Rostock, Germany (Prof. F. Liese)
• Madrid, Spain (Prof. L. Pardo)
• Leuven, Belgium (Prof. E.C. van der Meulen)
• Montpellier, France (Prof. A. Berlinet)
• Elche, Spain (Prof. D. Morales)
• Karlsruhe, Germany (Prof. W. Stummer)
• Waterloo, Canada (Prof. K.T. Wong)
• Helsinki, Finland (Prof. E. Oja)
• Baltimore, U.S.A. (Prof. J. Smid)
• Ilmenau, Germany (Prof. S. Vogel, Prof. C. Leibscher)
• Vilnius, Lithuania (Prof. V. Paulauskas, Prof. M. Bloznelis)

University Boards:

• I. Vajda is a chairman of the State Examination Committee at the Faculty of Physical and Nuclear Engineering and vice-chairman of the Board of doctoral studies at the same faculty, J.Á.Víšek is a dean of the Faculty of Social Sciences, Charles University and member of Scientific Board.
• Researchers of the Department are members of 3 different boards for defenses of doctoral theses at the Charles University, Faculty of Mathematics and Physics (Faculty of Social Sciences) and Czech Technical University.

Editorial Boards:

• Marie Hušková - Journal of Statistical Planning and Inference, Statistics, Applications of Mathematics, Sequential Analysis, American Mathematical Society
• Martin Janžura - Kybernetika, Statistical Inference for Stochastic Processes
• Petr Tichavský - IEEE Signal Processing Letters.
• Igor Vajda - Statistics and Decisions, Kybernetika, Applications of Mathematics, Journal of Statistical Planning and Inference
• Jan Ámos Víšek - Acta Universitatis Carolinae Oeconomica, Bulletin of the Czech Econometric Society.

Representation in International Societies:

• Marie Hušková - The Institute of Mathematical Statistics, American Statistical Association (ASA), International Statistical Institute, Bernoulli Society (Programme coordinator)
• Petr Lachout - member of American Mathematical Society
• Petr Tichavský - Institut of Eletrical and Electronics Engeneering
• I. Vajda - member of international committee European System Union, Institut of Eletrical and Electronics Engeneering, Institute of Mathematical Statistics
• Doc. RNDr J.Á. Víšek, CSc. - Bernoulli Society for Probability and Mathematical Statistics, International Association for Statistical Computing
• Petr Volf - Bernoulli Society for Mathematical Statistics and Probability, European Network for Business and Industrial Statistics

Recent Activities:

Grants and Projects:

• M. Hušková: Statistical models for structural changes and related problems III. (GA ČR, GA201/06/0186, 2006,-,2008).
• M. Hušková: Statistical dynamical models and their applications in economics, techniques and natural sciences (GD 201/05/H007, 2005,-,2008).
• M. Hušková: Detecting changes in time series (NATO, PST.EAP.CLG 980599, 2004,-,2006).
• M. Janžura: Probabilistic methods in the study of phase transitions of complex systems (GA ČR, GA201/06/1323, 2006,-,2008)
• I. Vajda: New results in testing the goodness-of-fit based in Pearson-type statistics (GA AV ČR, A\,1075403, 2004,-,2006)
• P. Volf: Intelligent information system of maintenance management (MO ČR, FI-IM3/036, 2006,-,2008)
• P. Volf: Spatial-temporal point processes and their applications (GA AV ČR, IAA101120604, 2006,-,2012), (co-investigator, together with MFF UK Praha)
• Research Center for Quality and Reliability of Production (MSM ČR, 1M06047, 2006,-,2009)
• Research Center Data, algorithms, decision making (MSM ČR, 1M0572, 2006,-,2009)

Teaching and Supervising Activities:

University Courses

36 courses on subjects related to the research field of the department were read.

• University of Economics: Probability theory and statistics (J.Á. Víšek); Advanced mathematical statistics (M. Hušková)
• Charles University - Faculty of Mathematics and Physics: Statistical seminar Bayesian methods, Probability and mathematical statistics, Sequential analysis, Sequential and Bayesian methods, Mathematical statistics, A Design of experiments, Probability and statistics, Sequential and Bayesian methods, Selected chapters of stochastics (M. Hušková); Advanced econometrics optimization, Advanced optimization and convex analysis, Introduction to optimization, Invariance principles, Mathematical proseminar of the Department of Statistics (P. Lachout); Stochastic differential equations, Seminar on stochastic evolution equations, Markov processes (J. Seidler); Seminar on probability and statistics (J. Swart)
• Charles University - Faculty of Social Sciences: Probability and mathematical statistics, Econometrics, Mathematical tools for capital markets, Statistics, Statistical data analysis, Advanced parts of econometrics (J.Á. Víšek)
• Charles University - Faculty of Science: Information theory (T. Marek)
• Czech Technical University - Faculty of Physical and Nuclear Engineering: Stochastic systems (M. Janžura); Quality control, Random processes (J. Michálek); Information theory (I. Vajda)
• Technical University Liberec: Applied Mathematics (P. Volf)
• The School of Professional Higher Education Chotěboř: Elements of mathematical statistics (J. Michálek)

Conferences:

Conferences - Organization:

Prague Stochastics 2006 a joint session of 7th Prague Symposium on Asymptotic Statistics and 15th Prague Conference on Information Theory, Statistical Decision Functions and Random Processes, Prague, August 21,-,25, 2006 (together with KPMS MFF UK, 169 participants, 130 abroad)

Conferences - Participations:

17 lectures, 3 of them invited, have been delivered at international conferences, including

• Tomáš Marek, Prague Stochastics 2006, a joint session of 7th Prague Symposium on Asymptotic Statistics and 15th Prague Conference on Information Theory, Statistical Decision Functions and Random Processes, Prague
• Lucie Fajfrová, Prague Stochastics 2006, a joint session of 7th Prague Symposium on Asymptotic Statistics and 15th Prague Conference on Information Theory, Statistical Decision Functions and Random Processes, Prague
• Petr Volf, Prague Stochastics 2006, a joint session of 7th Prague Symposium on Asymptotic Statistics and 15th Prague Conference on Information Theory, Statistical Decision Functions and Random Processes, Prague
• Petr Volf, Annual Conference of ENBIS, Wroclaw
• Igor Vajda, International Conference of France Statistical Society, Paris
• Marie Hušková, EMS 2006, Torun, Poland
• Marie Hušková, ROBUST 2006, Lhota nad Rohanovem
• Marie Hušková, PROBASTAT 2006, Smolenice
• Marie Hušková, Prague Stochastics 2006, a joint session of 7th Prague Symposium on Asymptotic Statistics and 15th Prague Conference on Information Theory, Statistical Decision Functions and Random Processes, Prague
• Petr Tichavský, Zbyněk Koldovský, IEEE Int. Conference on Acoustics, Speech and Signal Processing (ICASSP) Toulouse
• Lucie Fajfrová, 2nd International Workshop on Data -- Algorithms -- Decision Making, Třešť
• Tomáš Hobza, Prague Stochastics 2006, a joint session of 7th Prague Symposium on Asymptotic Statistics and 15th Prague Conference on Information Theory, Statistical Decision Functions and Random Processes, Prague
• David Kraus, Prague Stochastics 2006, a joint session of 7th Prague Symposium on Asymptotic Statistics and 15th Prague Conference on Information Theory, Statistical Decision Functions and Random Processes, Prague
• Zbyněk Pawlas, Prague Stochastics 2006, a joint session of 7th Prague Symposium on Asymptotic Statistics and 15th Prague Conference on Information Theory, Statistical Decision Functions and Random Processes, Prague
• Jan Swart, Prague Stochastics 2006, a joint session of 7th Prague Symposium on Asymptotic Statistics and 15th Prague Conference on Information Theory, Statistical Decision Functions and Random Processes, Prague
• Jan A. Víšek, Prague Stochastics 2006, a joint session of 7th Prague Symposium on Asymptotic Statistics and 15th Prague Conference on Information Theory, Statistical Decision Functions and Random Processes, Prague

Publications

UTIA library

Anotations

Blind Source Separation

Blind Source Separation consists of recovering original signals from their mixtures when the mixing process is unknown. In biomedicine, namely in MEG and EEG signal processing, one of the most popular algorithms nowadays is SOBI (Second Order Blind Identification). We proposed a procedure for fast implementation of the Weights-Adjusted SOBI (WASOBI) algorithm for asymptotically optimal separation of Gaussian autoregressive (AR) sources. The procedure employs fast computation of the optimum weight matrix, as well as an elaborate scheme for minimization of the associated weighted Least-Squares criterion. The resultant complexity is O(d^2M2+d^3M), where d is the number of sources and M is the required number of estimated correlation matrices. Our procedure allows separation of more than 100 sources in order of tens of seconds in Matlab. Simulations verify that the algorithm still attains the corresponding Cramér-Rao bound, even in these high dimensions.

Divergences and Informations in Statistics and Information Theory

Basic properties of f-divergences are proved in a new simpler manner. New relations to sufficiency and deficiency are established and new applications in estimation and testing are proposed. Statistical information of De Groot and the classical information of Shannon are shown to be extremal cases of a newly introduced class of so-called Arimoto informations.

Robustness of Median Estimator in Bernoulli Logistic Regression

The paper of T. Hobza and L. Pardo: On Robustness of Median Estimator in Bernoulli Logistic Regression published in the Proceedings of the Prague Stochastics 2006, presents generalized logistic regression models which include the classical model with binary responses governed by the Bernoulli law depending on the logistic regression function. The median estimator of the logistic regression parameters employing smoothed data in the discrete case, introduced in Hobza et al (2005), is considered. Sensitivity of this estimator to contaminations of the logistic regression data is studied by simulations and compared with the sensitivity of some robust estimators previously introduced to logistic regression. The median estimator is demonstrated to be more robust for higher levels of contamination.