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Analysis of retinal nerve fiber layer for diagnosis of glaucoma
Vodáková, Martina ; Malínský, Miloš (referee) ; Odstrčilík, Jan (advisor)
The master thesis is focused on creating a methodology for quantification of the nerve fiber layer on photographs of the retina. The introductory part of the text presents a medical motivation of the thesis and mentions several studies dealing with this issue. Furthermore, the work describes available textural features and compares their ability to quantify the thickness of the nerve fiber layer. Based on the described knowledge, the methodology to make different regression models enabling prediction of the retinal nerve fiber layer thickness was developed. Then, the methodology was tested on the available image dataset. The results showed, that the outputs of regression models achieve a high correlation between the predicted output and the retinal nerve fiber layer thickness measured by optical coherence tomography. The conclusion discusses an usability of the applied solution.
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Testing possibilities to extract selected landscape characteristics for description of indication-relevant bird species habitats in the Krkonoše Mts. from remote sensing data
Polák, Mojmír ; Kupková, Lucie (advisor) ; Janík, Tomáš (referee)
The thesis uses remote sensing data from two spatial scales (Sentinel-2 with a 10 x 10 m pixel and PlanetScope 3 x 3 m. It explores the possibilities of extracting selected landscape characteristics (spectral indices, land cover type, landscape metrics). In order to evaluate which characteristics and at what scale are statistically significant for the occurrence of 23 selected bird species, species richness in quadrats and the number of species of the order Passeriformes in the Krkonoše Mountains. Data on species occurrence were mapped in the year 2012-2014 The strength of the relationship between characteristics and abundance was determined by Pearson's correlation coefficient. It could not be confirmed that data with higher spatial resolution would be more beneficial for extracting landscape characteristics. Overall, the landscape characteristics did not prove functional relationships for all selected species, but for some species, species richness, and order of Passeriformes, the assumption of elevation and land cover as important factors was confirmed. Land cover was analysed using the Random Forest supervised classification method in Google Earth Engine with an overall accuracy of 78 % for Sentinel-2 data, both in tundra and in the rest of the area, and 77 % for PlanetScoce data in tundra, 66...
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Regression models in survival analysis and reliability
Novák, Petr ; Volf, Petr (advisor) ; Antoch, Jaromír (referee) ; Dohnal, Gejza (referee)
Regression models in survival analysis and reliability Doctoral thesis Petr Novák Charles University in Prague, Faculty of Mathematics and Physics Abstract: In present work we study methods for modeling the dependence of data from sur- vival and reliability setting on available explanatory variables. The first part of the work compares the properties of the Cox proportional hazards model, Aalen additive model and the Accelerated failure model for survival data. We present methods for testing goodness-of-fit based on counting processes and martingale theory, allowing to identify which model fits the data best. The second part focuses on modeling the lifetime of repairable systems. We study the means of incorporating the history of studied devices into the models, including the influence of corrective repairs and preventive maintenance actions. We demonstrate the introduced methods on real applications and study their properties in various situations on simulated data. 1
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Regression models and their teaching
Rybář, Marian ; Staněk, Jakub (referee) ; Kopa, Miloš (referee)
Title: "Regression models and their teaching" Author: Mgr. Marian Rybář Department: Department of Mathematics Education Abstract: Regression models and their outputs have a huge utilization not only in the field of medicine, science and managerial decision-making but also in many other fields. From the math didactics point of view is a question of intelligible explanation of regression models to non- math students very topical and exploitable theme. The main problem is an understandable explanation of this topic to statistics schooling members with minimal math application. These people aren't usually math or technical branch alumni, but they use regression models in their work. This work tries to suggest simply and clearly explanation of regression models on particular examples. Practical examples show the effects of the most common mistakes that are made by laymen in application of regression models. The main output of this work is a set of examples that could be used in regression models schooling. Keywords: regression models, regression analysis, didactics, teaching
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Maximum likelihood theory for not i.i.d. observations
Kielkowská, Eva ; Omelka, Marek (advisor) ; Pešta, Michal (referee)
Maximum likelihood approach for independent but not identically distributed observations is studied. In the first part of the thesis, conditions for consistency and asymptotic normality of the maximum likelihood estimates for this case are stated. Uniform integrability has a major role in proving the desired properties. K-sample problem serves as an example for using the described method. The second part is focused on estimates obtained by minimizing convex functions. Convexity is a key for showing the consistency and asymptotic normality of the estimates in this case. The results can be used for maximum likelihood when observations with logconcave densities are involved. Finally, normal linear model, logistic regression and Poisson regression examples are provided to present the application of the method.
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Regression models in survival analysis and reliability
Novák, Petr ; Volf, Petr (advisor) ; Antoch, Jaromír (referee) ; Dohnal, Gejza (referee)
Regression models in survival analysis and reliability Doctoral thesis Petr Novák Charles University in Prague, Faculty of Mathematics and Physics Abstract: In present work we study methods for modeling the dependence of data from sur- vival and reliability setting on available explanatory variables. The first part of the work compares the properties of the Cox proportional hazards model, Aalen additive model and the Accelerated failure model for survival data. We present methods for testing goodness-of-fit based on counting processes and martingale theory, allowing to identify which model fits the data best. The second part focuses on modeling the lifetime of repairable systems. We study the means of incorporating the history of studied devices into the models, including the influence of corrective repairs and preventive maintenance actions. We demonstrate the introduced methods on real applications and study their properties in various situations on simulated data. 1
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Regression models and their teaching
Rybář, Marian ; Staněk, Jakub (referee) ; Kopa, Miloš (referee)
Title: "Regression models and their teaching" Author: Mgr. Marian Rybář Department: Department of Mathematics Education Abstract: Regression models and their outputs have a huge utilization not only in the field of medicine, science and managerial decision-making but also in many other fields. From the math didactics point of view is a question of intelligible explanation of regression models to non- math students very topical and exploitable theme. The main problem is an understandable explanation of this topic to statistics schooling members with minimal math application. These people aren't usually math or technical branch alumni, but they use regression models in their work. This work tries to suggest simply and clearly explanation of regression models on particular examples. Practical examples show the effects of the most common mistakes that are made by laymen in application of regression models. The main output of this work is a set of examples that could be used in regression models schooling. Keywords: regression models, regression analysis, didactics, teaching
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Analysis of retinal nerve fiber layer for diagnosis of glaucoma
Vodáková, Martina ; Malínský, Miloš (referee) ; Odstrčilík, Jan (advisor)
The master thesis is focused on creating a methodology for quantification of the nerve fiber layer on photographs of the retina. The introductory part of the text presents a medical motivation of the thesis and mentions several studies dealing with this issue. Furthermore, the work describes available textural features and compares their ability to quantify the thickness of the nerve fiber layer. Based on the described knowledge, the methodology to make different regression models enabling prediction of the retinal nerve fiber layer thickness was developed. Then, the methodology was tested on the available image dataset. The results showed, that the outputs of regression models achieve a high correlation between the predicted output and the retinal nerve fiber layer thickness measured by optical coherence tomography. The conclusion discusses an usability of the applied solution.
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Hlavní inflační faktory v České republice
Kraváčková, Lenka
The bachelor thesis deals with the main inflationary factors and their changes caused by the onset of the economic crisis. It is focused on the time series analysis of selected macroeconomic data using Gretl software package. To determine main inflationary factors, two-variable and multiple regression models are created. The results prove that the most sigificant foreign factors are commodity prices, which limits monetary policy effects. However, the most important domestic factors have been changed from product and wages to M2 monetary aggregate and inflation expectations. The results form the basis for discussion and prove that the inflationary factors change over time.
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