|
| |
|
|
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
|
|
|
Deterministic and Stochastic Epidemic Models
Staněk, Jakub ; Štěpán, Josef (advisor) ; Hlubinka, Daniel (referee) ; Dohnal, Gejza (referee)
Kermack-McKendrick model and its version with vaccination are presented. First, we introduce a model with vaccination and then a numerical study that includes comparison of di erent vaccination strategies and searching for optimal vaccination strategy is presented. We proceed to introduce a stochastic model with migration and consequently we suggest its generalization and prove the existence and uniqueness of a solution to the stochastic di erential equation (henceforth SDE) describing this model. Three stochastic versions of Kermack-McKendrick model with vaccination are suggested and compared. A procedure of nding the optimal vaccination strategy is presented. We also prove the theorem on the existence and uniqueness of a solution to the SDE that drives a model with multiple pathogens. Finally, the stochastic di erential equation describing the general model is presented. We study properties of a solution to this SDE and present sufficient conditions for the existence of a solution that is absorbed by the natural barrier of the model.
|
|
|
Statistical image analysis in quality control
Legát, David ; Antoch, Jaromír (advisor) ; Dohnal, Gejza (referee) ; Tunák, Maroš (referee)
Title: Statistical image analysis in quality control Author: David Legát Department: Department of probability and mathematical statistics Supervisor: Prof. RNDr. Jaromír Antoch, CSc. Abstract: Currently, necessity to handle unstructured data rises significantly. One important area of unstructured data manipulation is signal processing such as audio and video, for which there exist many procedures. This work deals with the statistical approach to image processing, in which the image is interpreted as a representative of a random field. It describes two problems: removing noise from an image which facilitates better interpretation of the image, and image classification, in which we try to identify and recognize objects displayed. Part of the work aimed at eliminating of noise deals primarily with the use of MCMC simulation methods. These procedures can be tested in software that is included. Part of the work dealing with the classification of the image describes various modifications of classification trees methods. An example of image processing, which is the identification of defects in woven fabrics, is presented at the end. 1
|
|
|
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
|
|
|
Morpho-Colorimetric and Non-Parametric Analyses in Statistical Classification of Vascular Flora (Classification in Image Analysis)
Frigau, Luca ; Antoch, Jaromír (advisor) ; Dohnal, Gejza (referee) ; Wilhelm, Adalbert F.X. (referee)
Luca Frigau Abstract of PhD thesis This dissertation deals with statistical methodologies to apply to morphological classification of seeds through extracting information directly from their digital images. It concentrates more on the classifi- cation task, trying to enhance the quality of prediction, and on the automatizing of the classification process. These tasks are very important in botany because they avoid human contradictions in seed classification and to save a lot of time to specialized botanists. Firstly we focused on describing all stages necessary to move from a picture containing raw information of scanned objects to a data matrix usable as input for further statistical analyses. We illustrated how to convert an image so as to enhance its inner contrast in order to get easier the image segmentation. It has been introduced an approach that adapts a widely used method for detecting moving objects from video, called background subtraction (foreground detection), to image segmentation framework. It has been shown how it assists segmentation process to get good results, and allows to automate the process when foreground color of images is not constant, as well as speeding it up significantly. Then methods for enhancing quality of objects and removing residual noise have been illustrated. At the end of...
|
|
|
Statistical image analysis in quality control
Legát, David ; Antoch, Jaromír (advisor) ; Dohnal, Gejza (referee) ; Tunák, Maroš (referee)
Title: Statistical image analysis in quality control Author: David Legát Department: Department of probability and mathematical statistics Supervisor: Prof. RNDr. Jaromír Antoch, CSc. Abstract: Currently, necessity to handle unstructured data rises significantly. One important area of unstructured data manipulation is signal processing such as audio and video, for which there exist many procedures. This work deals with the statistical approach to image processing, in which the image is interpreted as a representative of a random field. It describes two problems: removing noise from an image which facilitates better interpretation of the image, and image classification, in which we try to identify and recognize objects displayed. Part of the work aimed at eliminating of noise deals primarily with the use of MCMC simulation methods. These procedures can be tested in software that is included. Part of the work dealing with the classification of the image describes various modifications of classification trees methods. An example of image processing, which is the identification of defects in woven fabrics, is presented at the end. 1
|
|
|
Deterministic and Stochastic Epidemic Models
Staněk, Jakub ; Štěpán, Josef (advisor) ; Hlubinka, Daniel (referee) ; Dohnal, Gejza (referee)
Kermack-McKendrick model and its version with vaccination are presented. First, we introduce a model with vaccination and then a numerical study that includes comparison of di erent vaccination strategies and searching for optimal vaccination strategy is presented. We proceed to introduce a stochastic model with migration and consequently we suggest its generalization and prove the existence and uniqueness of a solution to the stochastic di erential equation (henceforth SDE) describing this model. Three stochastic versions of Kermack-McKendrick model with vaccination are suggested and compared. A procedure of nding the optimal vaccination strategy is presented. We also prove the theorem on the existence and uniqueness of a solution to the SDE that drives a model with multiple pathogens. Finally, the stochastic di erential equation describing the general model is presented. We study properties of a solution to this SDE and present sufficient conditions for the existence of a solution that is absorbed by the natural barrier of the model.
|
|
| |
|
|
Implementation and Application of Statistical Methods in Research, Manufacturing Technology and Quality Control
Kupka, Karel ; Šeda, Miloš (referee) ; Militký, Jiří (referee) ; Dohnal, Gejza (referee) ; Karpíšek, Zdeněk (advisor)
This thesis deals with modern statistical approaches and their application aimed at robust methods and neural network modelling. Selected methods are analyzed and applied on frequent practical problems in czech industry and technology. Topics and methods are to be benificial in real applications compared to currently used classical methods. Applicability and effectivity of the algorithms is verified and demonstrated on real studies and problems in czech industrial and research bodies. The great and unexploited potential of modern theoretical and computational capacity and the potential of new approaces to statistical modelling and methods. A significant result of this thesis is also an environment for software application development for data analysis with own programming language DARWin (Data Analysis Robot for Windows) for implemenation of effective numerical algorithms for extaction information from data. The thesis should be an incentive for boarder use of robust and computationally intensive methods as neural networks for modelling processes, quality control and generally better understanding of nature.
|
guest ::
RSS feed.