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Stochastic Differential Equations with Gaussian Noise
Janák, Josef ; Maslowski, Bohdan (advisor) ; Duncan, Tyrone E. (referee) ; Pawlas, Zbyněk (referee)
Title: Stochastic Differential Equations with Gaussian Noise Author: Josef Janák Department: Department of Probability and Mathematical Statistics Supervisor: Prof. RNDr. Bohdan Maslowski, DrSc., Department of Probability and Mathematical Statistics Abstract: Stochastic partial differential equations of second order with two un- known parameters are studied. The strongly continuous semigroup (S(t), t ≥ 0) for the hyperbolic system driven by Brownian motion is found as well as the formula for the covariance operator of the invariant measure Q (a,b) ∞ . Based on ergodicity, two suitable families of minimum contrast estimators are introduced and their strong consistency and asymptotic normality are proved. Moreover, another concept of estimation using "observation window" is studied, which leads to more families of strongly consistent estimators. Their properties and special cases are descibed as well as their asymptotic normality. The results are applied to the stochastic wave equation perturbed by Brownian noise and illustrated by several numerical simula- tions. Keywords: Stochastic hyperbolic equation, Ornstein-Uhlenbeck process, invariant measure, paramater estimation, strong consistency, asymptotic normality.
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Parameter estimation of gamma distribution
Zahrádková, Petra ; Kulich, Michal (advisor) ; Hlávka, Zdeněk (referee)
It is well-known that maximum likelihood (ML) estimators of the two parame- ters in a Gamma distribution do not have closed forms. The Gamma distribution is a special case of a generalized Gamma distribution. Two of the three likeli- hood equations of the generalized Gamma distribution can be used as estimating equations for the Gamma distribution, based on which simple closed-form estima- tors for the two Gamma parameters are available. Intuitively, performance of the new estimators based on likelihood equations should be close to the ML estima- tors. The study consolidates this conjecture by establishing the asymptotic beha- viours of the new estimators. In addition, the closed-forms enable bias-corrections to these estimators. 1
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Neural Model of Transmission Channel in 60 Ghz ISM Band
Kotol, Martin
In this paper, methodology of estimating parameters of a wireless transmission channel inside a car is presented. The work is focused on the utilization of artificial neural networks for channel modelling in the frequency range from 55 GHz to 65 GHz. Promising results have been reached by a feed-forward neural network and a radial basis function neural network. In order to train the networks, a wireless transmission was carefully measured in a testing car. Measured data were properly processed to be used both for training neural networks and validating neural models.
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On the Optimization of Initial Conditions for a Model Parameter Estimation
Matonoha, Ctirad ; Papáček, Š. ; Kindermann, S.
The design of an experiment, e.g., the setting of initial conditions, strongly influences the accuracy of the process of determining model parameters from data. The key concept relies on the analysis of the sensitivity of the measured output with respect to the model parameters. Based on this approach we optimize an experimental design factor, the initial condition for an inverse problem of a model parameter estimation. Our approach, although case independent, is illustrated at the FRAP (Fluorescence Recovery After Photobleaching) experimental technique. The core idea resides in the maximization of a sensitivity measure, which depends on the initial condition. Numerical experiments show that the discretized optimal initial condition attains only two values. The number of jumps between these values is inversely proportional to the value of a diffusion coefficient D (characterizing the biophysical and numerical process). The smaller value of D is, the larger number of jumps occurs.
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GOF tests for gamma distribution
Klička, Petr ; Hlávka, Zdeněk (advisor) ; Kulich, Michal (referee)
The Bachelor thesis deals with the goodness of fit test for the Gamma distribution. Initially, we show several ways how to estimate the parameters of the Gamma distribution - firstly, the maximum likelihood estimator is presented, followed by estimator gained by the method of moments and fi- nally, we introduce the new estimator based on the sample covariance. The last estimator is used for constructing the goodness of fit test for the Gamma distribution. We define the test statistics V ∗ n to this test and its asymptotic normality is derived under the assumption of the null hypothesis. At the end of the thesis the simulations are realized to obtain the empirical size of the test for various values of parameter a and parameter b which equals one. 1
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Utilization of GRID technology in processing of medical information
Kulhánek, Tomáš ; Šárek, Milan (advisor) ; Kittnar, Otomar (referee) ; Anjum, Ashiq (referee)
This thesis focuses on selected areas of biomedical research in order to benefit from current computational infrastructures established in scientific community in european and global area. The theory of computation, parallelism and distributed computing, with focus on grid computing and cloud computing, is briefly introduced. Exchange of medical images was studied and a seamless integration of grid-based PACS system was established with the current distributed system in order to share DICOM medical images. Voice science was studied and access to real-time voice analysis application via remote desktop technology was introduced using customized protocol to transfer sound recording. This brings a possibility to access current legacy application remotely by voice specialists. The systems biology approach within domain of human physiology and pathophysiology was studied. Modeling methodology of human physiology was improved in order to build complex models based on acausal and object-oriented modeling techniques. Methods for conducting a parameter study (especially parameter estimation and parameter sweep) were introduced using grid computing and cloud computing technology. The identification of parameters gain substantial speedup by utilizing cloud computing deployment when performed on medium complex models of...
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Spatial point process with interactions
Vícenová, Barbora ; Beneš, Viktor (advisor) ; Zikmundová, Markéta (referee)
This thesis deals with the estimation of model parameters of the interacting segments process in plane. The motivation is application on the system of stress fibers in human mesenchymal stem cells, which are detected by fluorescent microscopy. The model of segments is defined as a spatial Gibbs point process with marks. We use two methods for parameter estimation: moment method and Takacs-Fiksel method. Further, we implement algorithm for these estimation methods in software Mathematica. Also we are able to simulate the model structure by Markov Chain Monte Carlo, using birth-death process. Numerical results are presented for real and simulated data. Match of model and data is considered by descriptive statistics. Powered by TCPDF (www.tcpdf.org)
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Sampling from finite population in economic problems
Krepl, Jan ; Červinka, Michal (advisor) ; Kraicová, Lucie (referee)
Survey sampling constitutes a basic method of obtaining values of population parameters. Social sciences including economics use survey sampling to collect information which is then used for research purposes. The goal of this thesis is to describe sample surveys in general and to focus on basic probability sampling schemes. For the empirical part, the author selected several suitable theses of IES FSV UK students where sample survey data was used. These theses serve as an illustration of described methods in theoretical part. At the end, the possibility of applications of probability sampling is discussed. Powered by TCPDF (www.tcpdf.org)
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Electrical impedance tomography of soft tissue
Pšenka, Marek ; Průša, Vít (advisor) ; Velímský, Jakub (referee)
Electrical impedance tomography of soft tissue This bachelor thesis presents an overview of electrical impedance tomography (EIT) as a proposed imaging technique with special focus on its applications in medicine. Amongst all of the areas being considered, the possibility of performing breast cancer examinations is given special focus. The author dicusses the motivation and rationale behind using EIT for this particular purpose and has gathered information about EIT systems which have been constructed to date. The reconstruction of a conductivity distribution within a physical body is a complex problem which necessitates the solution of a number of subproblems - starting with the calculation of these potential distribution within the body ending with the solution of an inverse boundary value problem. The thesis describes some aspects of these subproblems and presents their mathematical treatment. It concludes by testing the EIDORS software package which represents a reference implementation of algorithms for the EIT problem. 1
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