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Sequential Monte Carlo Methods
Sobková, Eva ; Zikmundová, Markéta (advisor) ; Prokešová, Michaela (referee)
Monte Carlo methods are used for stochastic systems simulations. Sequential Monte Carlo methods take advantage of the fact that observations are coming sequentially. This allows us to refine our estimate sequentially in time We introduce a State Space Model as a Hidden Markov Model. We describe Perfect Monte Carlo Sampling, Importance Sampling, Sequential Importance Sampling and discuss advantages and disadvantages of these methods. This discussion brings us to add a resampling step in Sequential Importance Sampling and introduce Particle Filter and Particle Marginal Metropolis-Hastings algorithm. We choose a Hidden Markov Model used for stochastic volatility modeling and make a simulation study in Wolfram Mathematica, version 8.
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Methods for Constrained State Estimation: Comparison and Application to Zero-Bound Interest Rate Problem
Musil, Karel ; Hlávka, Zdeněk (referee)
The thesis introduces an overview of techniques for filtering of unobserved variables using a state-space representation of a model and state inequality constraints. It is mainly aimed at a derivation of the linear Kalman filter and imposing state constraints. The state uniform model with noise bounds and the sequential importance sampling, as a method of particle filters using Monte Carlo simulations, are described as alternative methods. These three methods are applied on a simple semi-structural model for a monetary policy analysis. The filtration is based on Czech macroeconomic data and reflects an imposed time-varying non-negative state constraint on the nominal interest rate. Results of the algorithms are compared and discussed. Powered by TCPDF (www.tcpdf.org)
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Kernel Methods in Particle Filtering
Coufal, David ; Beneš, Viktor (advisor)
Kernel Methods in Particle Filtering David Coufal Doctoral thesis - abstract The thesis deals with the use of kernel density estimates in particle filtering. In particular, it examines the convergence of the kernel density estimates to the filtering densities. The estimates are constructed on the basis of an out- put from particle filtering. It is proved theoretically that using the standard kernel density estimation methodology is effective in the context of particle filtering, although particle filtering does not produce random samples from the filtering densities. The main theoretical results are: 1) specification of the upper bounds on the MISE error of the estimates of the filtering densities and their partial derivatives; 2) specification of the related lower bounds and 3) providing a suitable tool for checking persistence of the Sobolev character of the filtering densities over time. In addition, the thesis also focuses on designing kernels suitable for practical use. 1
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Moving Objects Detection in Video Sequences
Němec, Jiří ; Herout, Adam (referee) ; Španěl, Michal (advisor)
This thesis deals with methods for the detection of people and tracking objects in video sequences. An application for detection and tracking of players in video recordings of sport activities, e.g. hockey or basketball matches, is proposed and implemented. The designed application uses the combination of histograms of oriented gradients and classification based on SVM (Support Vector Machines) for detecting players in the picture. Moreover, a particle filter is used for tracking detected players. The whole system was fully tested and the results are shown in the graphs and tables with verbal descriptions.
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Compressive sampling for effective target tracking in a sensor network
Klimeš, Ondřej ; Veselý, Vítězslav (referee) ; Rajmic, Pavel (advisor)
The master's thesis deals with target tracking. For this a decentralized sensor network using distributed particle filter with likelihood consensus is used. This consensus is based on a sparse representation of local likelihood function in a suitable chosen dictionary. In this thesis two dictionaries are compared: the widely used Fourier dictionary and our proposed B-splines. At the same time, thanks to the sparsity of distributed data, it is possible to implement compressed sensing method. The results are compared in terms of tracking error and communication costs. The thesis also contains scripts and functions in MATLAB.
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Kernel Methods in Particle Filtering
Coufal, David ; Beneš, Viktor (advisor)
Kernel Methods in Particle Filtering David Coufal Doctoral thesis - abstract The thesis deals with the use of kernel density estimates in particle filtering. In particular, it examines the convergence of the kernel density estimates to the filtering densities. The estimates are constructed on the basis of an out- put from particle filtering. It is proved theoretically that using the standard kernel density estimation methodology is effective in the context of particle filtering, although particle filtering does not produce random samples from the filtering densities. The main theoretical results are: 1) specification of the upper bounds on the MISE error of the estimates of the filtering densities and their partial derivatives; 2) specification of the related lower bounds and 3) providing a suitable tool for checking persistence of the Sobolev character of the filtering densities over time. In addition, the thesis also focuses on designing kernels suitable for practical use. 1
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Kernel Methods in Particle Filtering
Coufal, David ; Beneš, Viktor (advisor) ; Klebanov, Lev (referee) ; Studený, Milan (referee)
Kernel Methods in Particle Filtering David Coufal Doctoral thesis - abstract The thesis deals with the use of kernel density estimates in particle filtering. In particular, it examines the convergence of the kernel density estimates to the filtering densities. The estimates are constructed on the basis of an out- put from particle filtering. It is proved theoretically that using the standard kernel density estimation methodology is effective in the context of particle filtering, although particle filtering does not produce random samples from the filtering densities. The main theoretical results are: 1) specification of the upper bounds on the MISE error of the estimates of the filtering densities and their partial derivatives; 2) specification of the related lower bounds and 3) providing a suitable tool for checking persistence of the Sobolev character of the filtering densities over time. In addition, the thesis also focuses on designing kernels suitable for practical use. 1
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Sequential Monte Carlo Methods
Sobková, Eva ; Zikmundová, Markéta (advisor) ; Prokešová, Michaela (referee)
Monte Carlo methods are used for stochastic systems simulations. Sequential Monte Carlo methods take advantage of the fact that observations are coming sequentially. This allows us to refine our estimate sequentially in time We introduce a State Space Model as a Hidden Markov Model. We describe Perfect Monte Carlo Sampling, Importance Sampling, Sequential Importance Sampling and discuss advantages and disadvantages of these methods. This discussion brings us to add a resampling step in Sequential Importance Sampling and introduce Particle Filter and Particle Marginal Metropolis-Hastings algorithm. We choose a Hidden Markov Model used for stochastic volatility modeling and make a simulation study in Wolfram Mathematica, version 8.
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Methods for Constrained State Estimation: Comparison and Application to Zero-Bound Interest Rate Problem
Musil, Karel ; Hlávka, Zdeněk (referee)
The thesis introduces an overview of techniques for filtering of unobserved variables using a state-space representation of a model and state inequality constraints. It is mainly aimed at a derivation of the linear Kalman filter and imposing state constraints. The state uniform model with noise bounds and the sequential importance sampling, as a method of particle filters using Monte Carlo simulations, are described as alternative methods. These three methods are applied on a simple semi-structural model for a monetary policy analysis. The filtration is based on Czech macroeconomic data and reflects an imposed time-varying non-negative state constraint on the nominal interest rate. Results of the algorithms are compared and discussed. Powered by TCPDF (www.tcpdf.org)
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Optimal methods for sparse data exchange in sensor networks
Valová, Alena ; Poměnková, Jitka (referee) ; Rajmic, Pavel (advisor)
This thesis is focused on object tracking by a decentralized sensor network using fusion center-based and consensus-based distributed particle filters. The model includes clutter as well as missed detections of the object. The approach uses sparsity of global likelihood function, which, by means of appropriate sparse approximation and the suitable dictionaty selection can significantly reduce communication requirements in the decentralized sensor network. The master's thesis contains a design of exchange methods of sparse data in the sensor network and a comparison of the proposed methods in terms of accuracy and energy requirements.
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