
From John Graunt to Adolphe Quetelet: on the Origins Of Demography
Kalina, Jan
John Graunt (16201674) and Adolphe Quetelet (17961874) were two important personalities, who contributed to the origins of demography. As they both developed statistical techniques for the analysis of demographic data, they are important also from the point of view of history of statistics. The contributions of both Graunt and Quetelet especially to the development of mortality tables and models are recalled in this paper. Already from the 17th century, the available mortality tables were exploited for computing life annuities. Also the contribution of selected personalities inspired by Graunt are recalled here, the work of Christian Huygens, Jacob Bernoulli, or Abraham de Moivre is discussed to document that the historical development of statistics and probability theory was connected with the development of demography.


Probabilistic representation of spatial fuzzy sets
Soukup, Lubomír
Membership function of a given fuzzy set is expressed by probability that a point belongs in the fuzzy set. Such a membership function is derived from probability distribution of points on the boundary of the fuzzy set. Polygonal boundary is considered. Spatial operations (conjunction, disjunction, complement) are defined accordingly. Several application areas are mentioned, namely classification of land cover, cadastral mapping, material quality analysis, interferometric monitoring of bridges.


Two Composition Operators for Belief Functions Revisited
Jiroušek, Radim ; Kratochvíl, Václav ; Shenoy, P. P.
In probability theory, compositional models are as powerful as Bayesian networks. However, the relation between belieffunction graphical models and the corresponding compositional models is much more complicated due to several reasons. One of them is that there are two composition operators for belief functions. This paper deals with their main properties and presents sufficient conditions under which they yield the same results.


Nonstandard dice sets
Chybová, Lucie ; Slavík, Antonín (advisor) ; Hlubinka, Daniel (referee)
The bachelor thesis discusses selected types of nonstandard dice sets with surprising and, in some cases, paradoxical properties. These dice are used in various gambling games, but they are also interesting from a purely theoretical perspective. The thesis focuses, one after another, on nontransitive, Lake Wobegon and Sicherman dice sets. When studying their properties, it mainly uses elementary probability theory and theory of cyclotomic polynomials. All the terms and results are demonstrated on examples. Powered by TCPDF (www.tcpdf.org)


The principle of antisuperposition in QM and the local solution of the Bell’s inequality problem
Souček, Jiří
In this paper we identify the superposition principle as a main source of problems in QM (measurement, collapse, nonlocality etc.). Here the superposition principle for individual systems is substituted by the antisuperposition principle: no nontrivial superposition of states is a possible individual state (for ensembles the superposition principle is true). The modified QM is based on the antisuperposition principle and on the new type of probability theory (Extended Probability Theory [1]), which allows the reversible Markov processes as models for QM. In the modified QM the measurement is a process inside of QM and the concept of an observation of the measuring system is defined. The outcome value is an attribute of the ensemble of measured systems. The collapse of the state is substituted by the Selection process. We show that the derivation of Bell’s inequalities is then impossible and thus QM remains a local theory. Our main results are: the locality of the modified QM, the local explanation of EPR correlations, the nonexistence of the waveparticle duality, the solution of the measurement problem. We show that QM can be understood as a new type of the statistical mechanics of manyparticle systems.
Fulltext: PDF


Transformations of random variables
Šára, Michal ; Marek, Luboš (advisor) ; Malá, Ivana (referee)
This bachelor thesis deals with the transformation of random variables,which plays a significant partv in the theory of probability. The main aim of this paper is to show few methods and techniques which are used when transforming random variables. At the very beginning of this paper one can find a definition and practical examples of the LebesgueStieltjes integral and probability measure, which are nowdays present in every book dealing with modern explanation of theory of probability.


Geometric probability
Březinová, Eliška ; Malá, Ivana (advisor) ; Čabla, Adam (referee)
This thesis deals with geometric probability applied on practical exercises. It covers Buffon's needle problem in detail; Laplace's conclusions about pi are supported by my own trial. Next, Bertrand's paradox is solved, and the conclusions are demonstrated on computer programs, which simulate the experiment. One chapter is dedicated to eight different exercises, which can be often found in textbooks. In the end we will mention practical usage of geometric probability, especially in the medicine field. We will point out to usage of modified Buffon's principle, which is used to estimate lengths of planar structures.


Basel II. and the calculation of the capital requirement relating to credit risk
Netolická, Klára ; Blahová, Naděžda (advisor)
The bachelor thesis focuses on the calculation of the capital requirement concerning credit risk from the perspective of the Basel II. capital agreement. Firstly, a broader framework is introduced, treating capital adequacy and the preceding concepts that were followed by the Basel II. approaches. Subsequently, the thesis deals with two alternative calculations between which banks can choose  the standardized approach and the internal ratings based approach, with an emphasis on the latter. The author proceeds from a general formulation of the calculation to its particular elements. Fairly detailed treatment is given to the inference of the risk weight function and to the methods of estimating the probability of default, one of the function's parameters.

 
 