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Introduction to Bayesian Data Analysis
Štádlerová, Kateřina ; Kulich, Michal (advisor) ; Anděl, Jiří (referee)
of the bachelor's thesis Title: Introduction to Bayesian Data Analysis Author: Kateřina Štádlerová Department: Department of Probability and Mathematical Statistics Supervisor: doc. Mgr. Michal Kulich, Ph.D., Department of Probability and Mathematical Statistics Abstract: The paper deals with basic principles of Bayesian methods. These me- thods have very broad range of use in statistical problems concerning estimation and hypothesis testing. However, their use is much wider; these methods are used in anti-spam filters of electronic mail or in the game theory. Definitions, theo- rems, proofs and examples are included in the paper for this purpose to enable easier understanding of particular topics. The paper is helpful mainly because of the fact that as yet there are not many books in Czech language dealing with Bayesian methods. 1
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Instruments for the Development of Rural Municipalities
Perlín, Radim ; Bičík, Ivan (advisor) ; Anděl, Jiří (referee) ; Vaishar, Antonín (referee)
Charles University in Prague Faculty of Science Department of Social Geography and Regional Development Radim Perlín Instruments for the Development of Rural Municipalities Summary Prague 2010 Gradual change in the functional utilisation of rural space is characteristic of the second half of the twentieth century. The original agrarian function of rural areas is losing its significance and rural areas and municipalities, along with their residents, are subsequently seeking new roles within society's division of functions. Following increases in rural population during the second half of the nineteenth century, caused by the demographic revolution, a portion of the economically active residents of rural areas emigrated over the next several decades, contributing to the rapid population growth of cities. Decreases in family size represent a consequence of the departure of a portion of rural inhabitants. Korčák studied the initial phases of these processes back in 1929. After World War II and in connection with the necessity to ensure food security and sufficient volume of agricultural production, the Common Agricultural Policy was formulated within the emerging European community as one of the first joint policies. It focuses primarily on ensuring sufficient income for agricultural workers, in the midst of...
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Nonnegative time series
Ročková, Veronika ; Anděl, Jiří (advisor) ; Štěpán, Josef (referee)
Models for non-negative time series nd their usefulness in many diverse areas of applications (hydrology, medicine, nance). The non-negative nature of the observations has been utilized for deriving estimators with superior asymptotic properties. For the purposes of estimation, it is necessary to recognize the situations when the estimated model indeed de nes a non-negative time series. Such non-negativity conditions can then be used as a basis for constrained optimization. The main thrust of this work is to review the non-negativity conditions currently available for ARMA models and, more importantly, to generalize the existing results for some models for which the explicit result was missing. We center our discussion mainly on univariate models. However, we note that the pursued ideas are directly applicable also for multivariate time series. This observation enables determination of some readily obtainable conditions for lower order vector valued Autoregressive Moving Average models.
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Prediction of transformed time series
Polák, Tomáš ; Jarušková, Daniela (referee) ; Anděl, Jiří (advisor)
The aim of this thesis is to find prediction for non-linear transformation of time series. First, under certain assumptions regarding the original time series, the autocovariance function and spectral density of the transformed time series are studied. General theorems are applied to concrete ARMA processes. Then general formulas for predictions of the transformed time series, which do not require knowledge of the autocovariance function of the transformed series nor its spectral density are presented. These formulas are applied to three concrete transformations and explicit formulas for ARMA processes are derived. Three types of predictions (optimal, naive and linear) are compared in the terms of proportional increase of mean square prediction error. Explicit formulas for ARMA processes are verified by a simulation.
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Application of Kalman Filtering
Svojík, Marek ; Anděl, Jiří (referee) ; Hlávka, Zdeněk (advisor)
The aim of this work is to discuss the use of the Kalman lter in some economical problems. Generally taken, the Kalman lter is a mathematical method (an algorithm) used for estimation of the non-observable component of a state. Especially, this approach will be applied to estimate the risk-neutral state price density of CALL options. In such case a non-linear relation between state and observed variables may be assumed, and the problem has to be linearized by Taylor expansion. In detail, the main Kalman ltering in the simple linear case will be presented in the rst chapter. In the second chapter, you can nd some application of that Kalman ltering in case of CALL options. The study of the extended Kalman lter and its application in case of a nonlinear state model and the use of the Taylor expansion can be found in Chapter 3. In the fourth chapter, we will be talking about estimating the risk-neutral price density of a CALL option. The corresponding outputs from the program R and the most important results of this work are summarized in the last Chapter 5.
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