Extremal dependence as given by the tail pairwise dependence matrix inprecipitation and temperature data

<p>A better understanding of the dynamics and impacts of extreme weather events and their changes due to climate change is the subject of the ClimXtreme project (climxtreme.net) funded by the German Federal Ministry of Education and Research. <br>The CoDEx project is investigating how data compression techniques can contribute to a better description and understanding of extremes. Various unsupervised learning approaches, such as clustering or principal component analysis, focusing on extremes have been developed recently and will be investigated and compared within the project. <br>We use principal component analysis to study the spatial (co-)occurrence during extreme weather events such as heavy precipitation, heat waves or droughts. The focus on extreme events is done by using the tail pairwise dependence matrix (TPDM), proposed by Cooley and Thibaud (2019) as an analogue to the covariance matrix for extremes. Since the simultaneous occurrence of precipitation deficits and high temperature played an important role, especially in heat waves, we explore how Cooley and Thibaud's concept can be used in this regard. We propose an estimation of the TPDM based on pairwise dependencies of two variables. A singular value decomposition gives us insight into the spatial co-occurrence of extreme spatial patterns, which contributes to the understanding of so-called compound events. <br>We use daily precipitation and temperature data, including observational stations and regional reanalyses in Germany and Europe. Using this method, we extract spatial patterns over Germany and Europe based on extreme dependencies. In addition, we identify historical events, and examine them in more detail in this context.</p>

Origin and variability of statistical dependencies between peak, volume, and duration of rainfall-driven flood events

Floods are among the most common and impactful natural events. The hazard of a flood event depends on its peak (Q), volume (V) and duration (D), which are interconnected to each other. Here, we used a worldwide dataset of daily discharge, two statistics (Kendall’s tau and Spearman’s rho) and a conceptual hydrological rainfall-runoff model as model-dependent realism, to investigate the factors controlling and the origin of the dependence between each couple of flood characteristics, with the focus to rainfall-driven events. From the statistical analysis of worldwide dataset, we found that the catchment area is ineffective in controlling the dependence between Q and V, while the dependencies between Q and D, and V and D show an increasing behavior with the catchment area. From the modeling activity, on the U.S. subdataset, we obtained that the conceptual hydrological model is able to represent the observed dependencies between each couple of variables for rainfall-driven flood events, and for such events, the pairwise dependence of each couple is not causal, is of spurious kind, coming from the “Principle of Common Cause”.

Grouping of genomic markers in populations with family structure

Background Linkage and linkage disequilibrium (LD) between genome regions cause dependencies among genomic markers. Due to family stratification in populations with non-random mating in livestock or crop, the standard measures of population LD such as $$r^2$$ r 2 may be biased. Grouping of markers according to their interdependence needs to account for the actual population structure in order to allow proper inference in genome-based evaluations. Results Given a matrix reflecting the strength of association between markers, groups are built successively using a greedy algorithm; largest groups are built at first. As an option, a representative marker is selected for each group. We provide an implementation of the grouping approach as a new function to the R package . This package enables the calculation of the theoretical covariance between biallelic markers for half- or full-sib families and the derivation of representative markers. In case studies, we have shown that the number of groups comprising dependent markers was smaller and representative SNPs were spread more uniformly over the investigated chromosome region when the family stratification was respected compared to a population-LD approach. In a simulation study, we observed that sensitivity and specificity of a genome-based association study improved if selection of representative markers took family structure into account. Conclusions Chromosome segments which frequently recombine in the underlying population can be identified from the matrix of pairwise dependence between markers. Representative markers can be exploited, for instance, for dimension reduction prior to a genome-based association study or the grouping structure itself can be employed in a grouped penalization approach.

Grouping of genomic markers in populations with family structure

Background : Linkage and linkage disequilibrium (LD) between genome regions cause dependencies among genomic markers. Due to family stratification in populations with non-random mating in livestock or crop, the standard measures of population LD such as r 2 may be biased. Grouping of markers according to their interdependence needs to account for the actual population structure in order to allow proper inference in genome-based evaluations. Results : Given a matrix reflecting the strength of association between markers, groups are built successively using a greedy algorithm; largest groups are built at first. As an option, a representative marker is selected for each group. We provide an implementation of the grouping approach as a new function to the R package hscovar. This package enables the calculation of the theoretical covariance between biallelic markers for half- or full-sib families and the calculation of representative markers. In case studies, we have shown that the number of groups comprising dependent markers was smaller and representative SNPs were spread more uniformly over the investigated chromosome region when the family stratification was respected compared to a population-LD approach. In a simulation study, we observed that sensitivity and specificity of a genome-based association study improved if selection of representative markers took family structure into account. Conclusions : Chromosome segments which frequently recombine in the underlying population can be identified from the matrix of pairwise dependence between markers. Representative markers can be exploited, for instance, for dimension reduction prior to a genome-based association study or the grouping structure itself can be employed in a grouped penalization approach.

Grouping of genomic markers in populations with family structure

Background: Linkage and linkage disequilibrium (LD) between genome regions cause dependencies among genomic markers. Due to family stratification in populations with non-random mating in livestock or crop, the standard measures of population LD such as r 2 may be biased. Grouping of markers according to their interdependence needs to account for the actual population structure in order to allow proper inference in genome-based evaluations. Results: Given a matrix reflecting the strength of association between markers, groups are built successively using a greedy algorithm; largest groups are built at first. As an option, a representative marker is selected for each group. We provide an implementation of the grouping approach as a new function to the R package hscovar. This package enables the calculation of the theoretical covariance between biallelic markers for half- or full-sib families and the calculation of representative markers. In case studies, we have shown that the number of groups comprising dependent markers was smaller and representative SNPs were spread more uniformly over the investigated chromosome region when the family stratification was respected compared to a population-LD approach. In a simulation study, we observed that sensitivity and specificity of a genome-based association study improved if selection of representative markers took family structure into account. Conclusions: Chromosome segments which frequently recombine in the underlying population can be identified from the matrix of pairwise dependence between markers. Representative markers can be exploited, for instance, for dimension reduction prior to a genome-based association study or the grouping structure itself can be employed in a grouped penalization approach.

Grouping of Genomic Markers in Populations With Family Structure

Background : Linkage and linkage disequilibrium (LD) between genome regions cause dependencies among genomic markers. Due to family stratification in populations with non-random mating in livestock or crop, the standard measures of population LD such as $r^2$ may be biased. Grouping of markers according to their interdependence needs to account for the actual population structure in order to allow proper inference in genome-based evaluations. Methods : he derivation of the covariance between markers in a population consisting of half- or full-sib families is described: it requires a genetic map and haplotype information of the common parent(s). A strategy, available in the literature, for grouping of markers based on a measure of population LD has been adapted to account for the dependence between markers if family stratification is present. Groups are built depending on the strength of association between markers; largest groups are built at first. As an option, a representative marker is selected for each group. Results : We provide an implementation of the theoretical covariance between biallelic markers for half- or full-sib families and the calculation of representative markers. In case studies, we have shown that the number of groups comprising dependent markers was smaller and representative SNPs were spread more uniformly over the investigated chromosome region when the family stratification was respected compared to a population-LD approach. In a simulation study, we observed that sensitivity and specificity of a genome-based association study improved if selection of representative markers took family structure into account. Conclusions : We offer an R~package for calculating the pairwise dependence between markers when family stratification is present. Chromosome segments which frequently recombine in the underlying population can be identified from the matrix of pairwise dependence between markers. Furthermore, grouping of genomic markers according to their interdependence is available. Representative markers can be exploited, for instance, for dimension reduction prior to a genome-based association study or the grouping structure itself can be employed in a grouped penalization approach.

Analyzing dependence matrices to investigate relationships between national football league combine event performances

The National Football League (NFL) Scouting Combine takes place annually for the purpose of allowing NFL teams to evaluate prospects. The battery of six physical tests receives a great deal of attention, and are a focus of team personnel as well as fans of NFL teams. Recently, some have suggested that the current battery of tests should be modified. This work aims to characterize the multivariate dependence structure between tests for Combine prospects, for both typical and elite-level performers, for the purpose of better understanding the current battery of tests before making modifications. Through analysis of two pairwise dependence matrices, one quantifying dependence in the center of the distribution and the other quantifying dependence in the tails of the distribution, this analysis finds that several events show differing levels of association, and that fewer Combine events may be sufficient going forward.