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Multivariate goodness-of-fit tests
Kuc, Petr ; Hlávka, Zdeněk (advisor) ; Antoch, Jaromír (referee)
In this thesis we introduce, implement and compare several multivariate goodness-of-fit tests. First of all, we will focus on universal mul- tivariate tests that do not place any assumptions on parametric families of null distributions. Thereafter, we will be concerned with testing of multi- variate normality and, by using Monte Carlo simulations, we will compare power of five different tests of bivariate normality against several alternati- ves. Then we describe multivariate skew-normal distribution and propose a new test of multivariate skew-normality based on empirical moment genera- ting functions. In the final analysis, we compare its power with other tests of multivariate skew-normality. 1
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Distance-based testing
Solnický, Radek ; Omelka, Marek (advisor) ; Komárek, Arnošt (referee)
When analyzing ecological data, one considers traditional multivariate techniques to be unsuitable. The use of dissimilarity coefficients and distance matrices is a way, how to solve this problem. In this work we present some of these coefficients and distance-based tests: Mantel test, several versions of ANOSIM and MRPP tests and distance-based test for homogeneity of multivariate dispersions. We focus on relationships among these tests and illustrate the use with an example. We also discuss the difficulties of interpretation of the results of these tests.
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Multivariate goodness-of-fit tests
Kuc, Petr ; Hlávka, Zdeněk (advisor) ; Antoch, Jaromír (referee)
In this thesis we introduce, implement and compare several multivariate goodness-of-fit tests. First of all, we will focus on universal mul- tivariate tests that do not place any assumptions on parametric families of null distributions. Thereafter, we will be concerned with testing of multi- variate normality and, by using Monte Carlo simulations, we will compare power of five different tests of bivariate normality against several alternati- ves. Then we describe multivariate skew-normal distribution and propose a new test of multivariate skew-normality based on empirical moment genera- ting functions. In the final analysis, we compare its power with other tests of multivariate skew-normality. 1
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Community ecology from the perspective of classic and bayesian statistics
Klimeš, Adam ; Keil, Petr (advisor) ; Herben, Tomáš (referee)
Community ecology from the perspective of classic and Bayesian statistics Ekologie společenstev z hlediska klasické a Bayesovské statistiky Řešitel: Adam Klimeš Vedoucí práce: Mgr. Petr Keil, Ph.D. Abstract Quantitative evaluation of evidence through statistics is a central part of present-day science. Bayesian approach represents an emerging but rapidly developing enrichment of statistical analysis. The approach differs in its foundations from the classic methods. These differences, such as the different interpretation of probability, are often seen as obstacles for acceptance of Bayesian approach. In this thesis I outline ways to deal with the assumptions of Bayesian approach, and I address the main objections against it. I present Bayesian approach as a new way to handle data to answer scientific questions. I do this from a standpoint of community ecology: I illustrate the novelty that Bayesian approach brings to data analysis of typical community ecology data, specifically, the analysis of multivariate datasets. I focus on principal component analysis, one of the typical and frequently used analytical techniques. I execute Bayesian analyses that are analogical to the classic principal components analysis, I report the advantages of the Bayesian version, such as the possibility of working with...
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Distance-based testing
Solnický, Radek ; Omelka, Marek (advisor) ; Komárek, Arnošt (referee)
When analyzing ecological data, one considers traditional multivariate techniques to be unsuitable. The use of dissimilarity coefficients and distance matrices is a way, how to solve this problem. In this work we present some of these coefficients and distance-based tests: Mantel test, several versions of ANOSIM and MRPP tests and distance-based test for homogeneity of multivariate dispersions. We focus on relationships among these tests and illustrate the use with an example. We also discuss the difficulties of interpretation of the results of these tests.
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