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Bivariate Functional Normalization of Methylation Array DataYacas, Clifford January 2021 (has links)
DNA methylation plays a key role in disease analysis, especially for studies that compare
known large scale differences in CpG sites, such as cancer/normal studies or between-tissues
studies. However, before any analysis can be done, data normalization and preprocessing of
methylation data are required. A useful data preprocessing pipeline for large scale comparisons
is Functional Normalization (FunNorm), (Fortin et al., 2014) implemented in the minfi
package in R. In FunNorm, the univariate quantiles of the methylated and unmethylated
signal values in the raw data are used to preprocess the data. However, although FunNorm
has been shown to outperform other preprocessing and data normalization processes for
these types of studies, it does not account for the correlation between the methylated and
unmethylated signals into account; the focus of this paper is to improve upon FunNorm by
taking this correlation into account. The concept of a bivariate quantile is used in this study
as an attempt to take the correlation between the methylated and unmethylated signals
into consideration. From the bivariate quantiles found, the partial least squares method is
then used on these quantiles in this preprocessing. The raw datasets used for this research
were collected from the European Molecular Biology Laboratory - European Bioinformatics
Institute (EMBL-EBI) website. The results from this preprocessing algorithm were then
compared and contrasted to the results from FunNorm. Drawbacks, limitations and future
research are then discussed. / Thesis / Master of Science (MSc)
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Medidas de assimetria bivariada e dependência local. / Measures of bivariate asymmetry and local dependence.Ferreira, Flavio Henn 03 October 2008 (has links)
Esta tese trata de dois assuntos importantes na teoria de risco: o fenômeno da dependência local e a identificação e mensuração de assimetrias apresentadas pelos dados. A primeira parte trata de dependência local, sendo abordadas algumas medidas já analisadas na literatura. Versões locais dos coeficientes de Kendall e Spearman , baseadas na distribuição condicional dos dados, são propostas. São apresentadas algumas propriedades dessas medidas e a aplicação das mesmas a algumas cópulas. Na segunda parte são apresentados resultados sobre cópulas bivariadas que são as menos associativas e menos bi-simétricas segundo o critério de máxima distância modular. A última parte trata da não-permutabilidade e assimetria radial dos dados. Uma medida de não-permutabilidade baseada nos coeficientes de correlação condicional é proposta e aplicada a algumas distribuições. No final, o conceito de quantil bivariado é aplicado nas definições de medidas para avaliar o grau de permutabilidade e de simetria radial presentes na estrutura de dependência dos dados e de testes de hipóteses para verificar se a cópula subjacente aos dados é permutável ou radialmente simétrica. / In this thesis two important fields in risk theory are studied: the local dependence phenomenon and the identification and measuring of asymmetries contained in data. The first part deals with local dependence: some measures already studied in the literature are presented and discussed, and local versions of the coefficients Kendall and Spearman , based on the conditional distribution of data, are proposed. Properties of these measures and some examples concerning its application are treated. In the second part are presented some results about bivariate copulas which are the least associative and the least bi-symmetric according to the maximum modular distance. The last part analyses the nonexchangeability and the radial asymmetry of data. A measure of nonexchangeability based on the conditional correlation coefficient is proposed and applied to some distribution functions. At the end, the concept of bivariate quantile is applied in the definitions of measures for evaluating the degree of exchangeability and radial symmetry present in data and of hypothesis tests proposed for verifying whether the underlying copula is exchangeable or radially symmetric.
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Medidas de assimetria bivariada e dependência local. / Measures of bivariate asymmetry and local dependence.Flavio Henn Ferreira 03 October 2008 (has links)
Esta tese trata de dois assuntos importantes na teoria de risco: o fenômeno da dependência local e a identificação e mensuração de assimetrias apresentadas pelos dados. A primeira parte trata de dependência local, sendo abordadas algumas medidas já analisadas na literatura. Versões locais dos coeficientes de Kendall e Spearman , baseadas na distribuição condicional dos dados, são propostas. São apresentadas algumas propriedades dessas medidas e a aplicação das mesmas a algumas cópulas. Na segunda parte são apresentados resultados sobre cópulas bivariadas que são as menos associativas e menos bi-simétricas segundo o critério de máxima distância modular. A última parte trata da não-permutabilidade e assimetria radial dos dados. Uma medida de não-permutabilidade baseada nos coeficientes de correlação condicional é proposta e aplicada a algumas distribuições. No final, o conceito de quantil bivariado é aplicado nas definições de medidas para avaliar o grau de permutabilidade e de simetria radial presentes na estrutura de dependência dos dados e de testes de hipóteses para verificar se a cópula subjacente aos dados é permutável ou radialmente simétrica. / In this thesis two important fields in risk theory are studied: the local dependence phenomenon and the identification and measuring of asymmetries contained in data. The first part deals with local dependence: some measures already studied in the literature are presented and discussed, and local versions of the coefficients Kendall and Spearman , based on the conditional distribution of data, are proposed. Properties of these measures and some examples concerning its application are treated. In the second part are presented some results about bivariate copulas which are the least associative and the least bi-symmetric according to the maximum modular distance. The last part analyses the nonexchangeability and the radial asymmetry of data. A measure of nonexchangeability based on the conditional correlation coefficient is proposed and applied to some distribution functions. At the end, the concept of bivariate quantile is applied in the definitions of measures for evaluating the degree of exchangeability and radial symmetry present in data and of hypothesis tests proposed for verifying whether the underlying copula is exchangeable or radially symmetric.
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