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Functional data and their principal components analysis
Kasanický, Ivan ; Hlubinka, Daniel (advisor) ; Hušková, Marie (referee)
Presented thesis deals with analysis of functional data. In the first part, problem which arises because of only finite possible numbers of observations is discussed. This problem is solved using representation by basis functions with emphasis on B-splines basis. The second part is focused on functional principal component analysis that could be understood as a natural extension of a multivariate case or as an application of Karhunen-Lo`eve expansion , which is based on Mercer's theorem. Estimations of principal components together with rates of convergence are mentioned too. Practical computation of principal components is mentioned in the last chapter.
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Ensemble Kalman filter on high and infinite dimensional spaces
Kasanický, Ivan ; Hlubinka, Daniel (advisor) ; Pannekoucke, Olivier (referee) ; Antoch, Jaromír (referee)
Title: Ensemble Kalman filter on high and infinite dimensional spaces Author: Mgr. Ivan Kasanický Department: Department of Probability and Mathematical Statistics Supervisor: doc. RNDr. Daniel Hlubinka, Ph.D., Department of Probability and Mathematical Statistics Consultant: prof. RNDr. Jan Mandel, CSc., Department of Mathematical and Statistical Sciences, University of Colorado Denver Abstract: The ensemble Kalman filter (EnKF) is a recursive filter, which is used in a data assimilation to produce sequential estimates of states of a hidden dynamical system. The evolution of the system is usually governed by a set of di↵erential equations, so one concrete state of the system is, in fact, an element of an infinite dimensional space. In the presented thesis we show that the EnKF is well defined on a infinite dimensional separable Hilbert space if a data noise is a weak random variable with a covariance bounded from below. We also show that this condition is su cient for the 3DVAR and the Bayesian filtering to be well posed. Additionally, we extend the already known fact that the EnKF converges to the Kalman filter in a finite dimension, and prove that a similar statement holds even in a infinite dimension. The EnKF su↵ers from a low rank approximation of a state covariance, so a covariance localization is required in...
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Functional data and their principal components analysis
Kasanický, Ivan ; Hlubinka, Daniel (advisor) ; Hušková, Marie (referee)
Presented thesis deals with analysis of functional data. In the first part, problem which arises because of only finite possible numbers of observations is discussed. This problem is solved using representation by basis functions with emphasis on B-splines basis. The second part is focused on functional principal component analysis that could be understood as a natural extension of a multivariate case or as an application of Karhunen-Lo`eve expansion , which is based on Mercer's theorem. Estimations of principal components together with rates of convergence are mentioned too. Practical computation of principal components is mentioned in the last chapter.
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Popis modelu TDD, verze 3.5
Konár, Ondřej ; Brabec, Marek ; Kasanický, Ivan ; Malý, Marek ; Pelikán, Emil
Zpráva obsahuje popis tvorby a použití modelu TDD pro odhad spotřeby zemního plynu zákazníků s měřením typu C. Součástí zprávy je metodika použití modelu TDD operátorem trhu, dále metodika použití TDD provozovatelem distribuční soustavy (PDS), popis aktualizace modelu TDD a popis předávaných souborů s parametry. Model je otestován na reálných datech ze zákaznického kmene distribuèní spoleènosti RWE GasNet a na datech z mimořádných průběhových měření. Dokument zahrnuje stav ke dni 15.10.2014.
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Statistical analysis and research on the links in the measured traffic data
Brabec, M. ; Konár, O. ; Kasanický, I. ; Pelikán, E. ; Přikryl, Jan
One of the current problems in transport research is the problem of availability of huge amounts of unused data measured telematics systems on motorways and urban roads. This data often contain information that - without the use of appropriate mathematical tools for data analysis - remain hidden and unused for traffic control. Within the project, a new method of traffic congestion in the urban areas, our aim is to propose new algorithms for adaptive control of urban transport networks. The current version of the algorithm is based on a linearized model of the development length of the queue of vehicles waiting at the red light, based on the classic balance of conservation. This model is for cases saturation supplemented alternative model queue length as a function of traffic occupancy detector. The aim of the work described in this report was to investigate possible links and other hidden states of the transport system, hidden in the measured data, and until now not considered by the traffic model used.
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