National Repository of Grey Literature 15 records found  previous11 - 15  jump to record: Search took 0.00 seconds. 
Bayesian and Maximum Likelihood Nonparametric Estimation in Monotone Aalen Model
Timková, Jana
This work is devoted to seeking methods for analysis of survival data with the Aalen model under special circumstances. We supposed, that all regres- sion functions and all covariates of the observed individuals were nonnegative and we named this class of models monotone Aalen models. To find estimators of the unknown regression functions we considered three maximum likelihood based approaches, namely the nonparametric maximum likelihood method, the Bayesian analysis using Beta processes as the priors for the unknown cumulative regression functions and the Bayesian analysis using a correlated prior approach, where the regression functions were supposed to be jump processes with a martingale structure. Powered by TCPDF (www.tcpdf.org)
EM algorithm
Vacula, Ondřej ; Komárek, Arnošt (advisor) ; Antoch, Jaromír (referee)
This paper discusses the EM algorithm. This algorithm is used, for example, to calculate maximum likelihood estimate of unknown parameter. The algorithm is based on repeated calculations of certain expected value and maximizing specific function. We begin with parameter estimation problem, describe the maximum likelihood method and concept of incomplete data. Then we formulate the EM algorithm and its properties. In the next chapter we apply this knowledge to three selected statistical problems. At first we examine standard mixture model, then the linear mixed model and finally we analyze censored data. Powered by TCPDF (www.tcpdf.org)
Expectation-Maximization Algorithm
Vichr, Jaroslav ; Pešta, Michal (advisor) ; Zvára, Karel (referee)
EM (Expectation-Maximization) algorithm is an iterative method for finding maximum likelihood estimates in cases, when either complete data include missing values or assuming the existence of additional unobserved data points can lead to more simple formulation of the model. Each of its iterations consists of two parts. During the E step (expectation) we calculate the expected value of the log-likelihood function of the complete data, with respect to the observed data and the current estimate of the parameter. The M step (maximization) then finds new estimate, which will maximize the function obtained in the previous step and which will be used in the next iteration in step E. EM algorithm has important use in e.g. price and manage risk of the portfolio.
Evolution of brain size in bats (Chiroptera)
Králová, Zuzana ; Němec, Pavel (advisor) ; Kratochvíl, Lukáš (referee)
According to the prevailing doctrine, brain size has mainly increased throughout the evolution of mammals and reductions in brain size were rare. On the other hand, energetic costs of developing and maintaining big brain are high, so brain size reduction should occur every time when the respective selective pressure is present. Modern phylogenetic methods make it possible to test the presence of evolutionary trend and to infer the ancestral values of the trait in question based on knowledge of phylogeny and trait values for recent species. However, this approach has been rarely applied to study brain evolution so far. In this thesis, I focus on bats (Chiroptera). Bats are a suitable group for demonstrating the importance of brain size reductions. Considering their energetically demanding mode of locomotion, they are likely to have been under selection pressure for brain reduction. Furthermore, there is a large amount of data on body and brain mass of recent species available. Finally, phylogenetic relationships among bats are relatively well resolved. My present study is based on body masses and brain masses of 334 recent bat species (Baron et al., 1996) and on a phylogeny obtained by adjusting existing bat supertree (Jones et al., 2002) according to recent molecular studies. Analysing the data for...
Extreme Value Distributions with Applications
Fusek, Michal ; Skalská,, Hana (referee) ; Karpíšek, Zdeněk (referee) ; Michálek, Jaroslav (advisor)
The thesis is focused on extreme value distributions and their applications. Firstly, basics of the extreme value theory for one-dimensional observations are summarized. Using the limit theorem for distribution of maximum, three extreme value distributions (Gumbel, Fréchet, Weibull) are introduced and their domains of attraction are described. Two models for parametric functions estimation based on the generalized extreme value distribution (block maxima model) and the generalized Pareto distribution (threshold model) are introduced. Parameters estimates of these distributions are derived using the method of maximum likelihood and the probability weighted moment method. Described methods are used for analysis of the rainfall data in the Brno Region. Further attention is paid to Gumbel class of distributions, which is frequently used in practice. Methods for statistical inference of multiply left-censored samples from exponential and Weibull distribution considering the type I censoring are developed and subsequently used in the analysis of synthetic musk compounds concentrations. The last part of the thesis deals with the extreme value theory for two-dimensional observations. Demonstrational software for the extreme value distributions was developed as a part of this thesis.

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