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Statistical analysis of ROC curves
Kutálek, David ; Bednář, Josef (referee) ; Michálek, Jaroslav (advisor)
The ROC (Receiver Operating Characteristic) curve is a projection of two different cumulative distribution functions F0 and F1. On axis are values 1-F0(c) and 1-F1(c). The c-parameter is a real number. This curve is useful to check quality of discriminant rule which classify an object to one of two classes. The criterion is a size of an area under the curve. To solve real problems we use point and interval estimation of ROC curves and statistical hypothesis tests about ROC curves.
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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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Optimality of sample variance
Gleta, Filip ; Kulich, Michal (advisor) ; Anděl, Jiří (referee)
It is widely known that the most common estimators of the variance and the standard deviation based on i.i.d. data are not optimal with respect to the mean squared error. The aim of this thesis is to study and summarize the various approaches to seeking an improved estimator, which stem mainly from the innovative ideas presented by Stein (1964). Taken into consideration is the point estimator of the variance and the standard deviation. Each of the improved estimators include, in addition to their construction, a discussion regarding admissibility with respect to the MSE. Subsequently, using simple simulations for various distributions, it is examined whether obtained improvements lead to better results in practice. Powered by TCPDF (www.tcpdf.org)
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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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Statistical analysis of ROC curves
Kutálek, David ; Bednář, Josef (referee) ; Michálek, Jaroslav (advisor)
The ROC (Receiver Operating Characteristic) curve is a projection of two different cumulative distribution functions F0 and F1. On axis are values 1-F0(c) and 1-F1(c). The c-parameter is a real number. This curve is useful to check quality of discriminant rule which classify an object to one of two classes. The criterion is a size of an area under the curve. To solve real problems we use point and interval estimation of ROC curves and statistical hypothesis tests about ROC curves.
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Estimated probability of unrepeatable events
Novák, Vít ; Hebák, Petr (advisor) ; Černý, Michal (referee)
Anywhere we see a prognostication system; we can run up against the need of evaluating it. For the evaluation is frequently used unsuitable methods. There are such cases where is need to correctly take effects of mistakes into consideration. And here we can use statistic based on information measure either entropy. The first part deals with this point of issue. In the second part I am trying to show possible areas of use, for example betting. I enclose practical remarks from this issue and the methods making these estimators, which are dependent on nature of issued events.
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