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Parameter estimation of random variables distribution
Šimková, Barbora ; Mošna, František (advisor) ; Novotná, Jarmila (referee)
of the bachelor's thesis Title: Parameter estimation of random variables distribution Author: Bc. Barbora Šimková Department: Department of Mathematics and Mathematical Education Supervisor: RNDr. František Mošna, Dr. Abstract: The subject of this thesis is to compare basic methods by which it is possible to calculate point estimates of discrete and continuous probability distributions. The work deals with the analysis of the two methods - the method of moments and maximum like- lihood method. These methods are used for point estimates of probability distributions parameters. The method of moments studies the comparison between the theoretical and sample moments of a random variable. The method of maximum likelihood is another alternative for the calculation of point estimates, which uses the classical ap- proach of finding the maximum of a function, using the properties of random selection. These methods of calculation are based on statistical methods and could be useful for extending the basic course on probability and statistics at Charles University's Fac- ulty of Education. The work is an overview of the estimated parameters of the basic distribution and compares the quality of two basic methods for their estimation. Keywords: parameter estimation, distribution of random variables, maximum...
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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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Interest Rates
Holotňáková, Dominika ; Hurt, Jan (advisor) ; Zichová, Jitka (referee)
This thesis is focused on the study of interest rates, It consists of four chapters. The first chapter provides introduction to this issue, presents basic terminology and different method of interest rate process. The second chapter re- presents theoretical one-factor and two-factor models of interest rates, it is mainly aimed at Vasicek, Dothan and Cox-Ingersoll-Ross model, which are used in the practical part. The third chapter is devoted to internal bank policy, describing the most important factors influencing amount of interest rate and credit limit. The last part of the paper is the practical application of one-factor models on real data. At the beginning of the chapter, we describe methods of parameters esti- mation, which are used for individual models. Numerically estimated parameters are inputs for simulations of yield curves by these models. 1
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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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Stochastic Differential Equations with Gaussian Noise
Janák, Josef ; Maslowski, Bohdan (advisor)
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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REGULATORY NETWORK OF DRUG-INDUCED ENZYME PRODUCTION: PARAMETER ESTIMATION BASED ON THE PERIODIC DOSING RESPONSE MEASUREMENT
Papáček, Štěpán ; Lynnyk, Volodymyr ; Rehák, Branislav
The common goal of systems pharmacology, i.e. systems biology applied to the eld of pharmacology, is to rely less on trial and error in designing an input-output systems, e.g. therapeutic schedules. In this paper we present, on the paradigmatic example of a regulatory network of drug-induced enzyme production, the further development of the study published by Duintjer Tebbens et al. (2019) in the Applications of Mathematics. Here, the key feature is that the nonlinear model in form of an ODE system is controlled (or periodically forced) by an input signal being a drug intake. Our aim is to test the model features under both periodic and nonrecurring dosing, and eventually to provide an innovative method for a parameter estimation based on the periodic dosing response measurement.
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Parameter Estimation in Stochastic Differential Equations
Pacák, Daniel ; Maslowski, Bohdan (advisor) ; Hlubinka, Daniel (referee)
In the Thesis the problem of estimating an unknown parameter in a stochastic dif- ferential equation is studied. Linear equations with Volterra process as the source of noise are considered. Firstly, the properties of Volterra processes and the properties of stochastic integral with respect to a Volterra process are presented. Secondly, the prop- erties of the solution to the equation under consideration are discussed. This includes the existence of the strictly stationary solution, the properties of such solution and ergodic results. These results are then generalized to equations with a mixed noise. Ergodic results are used to derive strongly consistent estimators of the unknown parameter. 1
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