Multivariate dependence measures and data analysis

Among bivariate tail dependence measures, the tail dependence coefficient has emerged as the popular choice. Akin to the correlation matrix, a multivariate dependence measure is constructed using these bivariate measures, and this is referred to in the literature as the tail dependence matrix (TDM). While the problem of determining whether a given d × d matrix is a correlation matrix is of the order O(d3) in complexity, determining if a matrix is a TDM (the realization problem) is believed to be non-polynomial in complexity. Using a linear programming (LP) formulation, we show that the combinatorial structure of the constraints is related to the intractable max-cut problem in a weighted graph. This connection provides an avenue for constructing parametric classes admitting a polynomial in d algorithm for determining membership in its constraint polytope. The complexity of the general realization problem is justifiably of much theoretical interest. Since in practice one resorts to lower dimensional parametrization of the TDMs, we posit that it is rather the complexity of the realization problem restricted to parametric classes of TDMs, and algorithms for it, that are more practically relevant. In this paper, we show how the inherent symmetry and sparsity in a parametrization can be exploited to achieve a significant reduction in the LP formulation, which can lead to polynomial complexity of such realization problems - some parametrizations even resulting in the constraint polytope being independent of d. We also explore the use of a probabilistic viewpoint on TDMs to derive the constraint polytopes.

Our aim was to evaluate liver transplant outcomes involving donors with high macrosteatosis grafts in the obese modern liver transplant recipient population. A high-steatosis graft was defined as donor graft macrosteatosis ≥30% on biopsy. Recipient obesity was defined as body mass index (BMI) >35 adjusted for ascites. Raw and adjusted recipient liver transplant survival were evaluated and compared between 4 cohorts: (1) high-steatosis graft in high-BMI recipient; (2) low-steatosis graft in high-BMI recipient; (3) high-steatosis graft in normal-BMI recipient; and (4) low-steatosis graft in normal-BMI recipient. After adjustment for multiple factors, recipient high-BMI remained an independent predictor of posttransplant mortality at 30 days (P < 0.0001) and persisted at 1 year (P = 0.009). A high-steatosis graft was the strongest independent predictor of mortality at 30 days (hazard ratio 2.05, 1.66-2.53; P < 0.0001) and that effect was diminished but persistent at 1 year (1.27, 1.10-1.46; P = 0.001). Recipient high-BMI and a high-steatosis graft are both significant independent and equally powerful predictors of mortality after modern liver transplant. High-steatosis grafts transplanted into obese recipients have the highest mortality. The increase in mortality associated with a high-steatosis graft into a normal-BMI recipient is similar in magnitude to a low-steatosis graft placed into a high-BMI recipient.

Summary The well-treatment program is an important part of the field-development plan, and certain variables, such as job-pause time (JPT) and fracture screenout, can affect its efficiency. JPT is the time during which pumping is paused between subsequent treatments of a job. Screenout occurs because of a sudden restriction of fluid flow inside the fracture and through the perforation. The objectives of this work are to investigate whether, from existing data, it is possible to find patterns in significant variables that affect the extreme values of JPT in a particular region, and what is the most critical variable causing screenout. The answers are sought by applying a classification-and-regression tree (CART) to both categorical and continuous variables in the database. The practical application of CART is presented by use of case studies containing JPT and screenout. Significant variables are found that affect the response variables, and predictor variables are ranked in the hierarchal order of their importance. Such information can be used to control predictor variables that cause high JPT or screenout. The results are outlined in an intuitive way, including categorical, continuous, and missing values. Because CART is a data-driven, deterministic model, one cannot calculate the confidence interval of the predicted response. The confidence in results is purely because of historical values, and the accuracy of the result produced by a tree model depends on the quality of recorded data measured in terms of volume, reliability, and consistency. The prediction capability of CART is enhanced by use of the normal-score transform and by dividing the data set into smaller groups by use of clustering. The approach presented in this paper analyzes a data set under limited information and high uncertainty and should lead to developing methodology for generating proxy models to find future success indices (e.g., one for drilling efficiency or production from a fracture). This could standardize stimulation and generate decision practices to save costs in field development and the optimization process.

Multivariate data analysis for Raman imaging of a model pharmaceutical tablet

In this paper, we develop improved rearrangement algorithms to find the dependence structure that minimizes a convex function of the sum of dependent variables with given margins. We propose a new multivariate dependence measure, which can assess the convergence of the rearrangement algorithms and can be used as a stopping rule. We show how to apply these algorithms for example to finding the dependence among variables for which the marginal distributions and the distribution of the sum or the difference are known. As an example, we can find the dependence between two uniformly distributed variables that makes the distribution of the sum of two uniform variables indistinguishable from a normal distribution. Using MCMC techniques, we design an algorithm that converges to the global optimum.

Neutrophil-to-lymphocyte ratio on admission is an independent risk factor for the severity and mortality in patients with coronavirus disease 2019

Standard multivariate analysis methods aim to identify and summarize the main structures in large data sets containing the description of a number of observations by several variables. In many cases, spatial information is also available for each observation, so that a map can be associated to the multivariate data set. Two main objectives are relevant in the analysis of spatial multivariate data: summarizing covariation structures and identifying spatial patterns. In practice, achieving both goals simultaneously is a statistical challenge, and a range of methods have been developed that offer trade-offs between these two objectives. In an applied context, this methodological question has been and remains a major issue in community ecology, where species assemblages (i.e., covariation between species abundances) are often driven by spatial processes (and thus exhibit spatial patterns). In this paper we review a variety of methods developed in community ecology to investigate multivariate spatial patterns. We present different ways of incorporating spatial constraints in multivariate analysis and illustrate these different approaches using the famous data set on moral statistics in France published by Andr\'{e}-Michel Guerry in 1833. We discuss and compare the properties of these different approaches both from a practical and theoretical viewpoint.

Calibration of Cystatin C in the National Health and Nutrition Examination Surveys (NHANES)

It is well known that the correlation matrix has a central role in the analysis of multivariate data. The inverse of the correlation matrix, however, also has important interpretations. An exposition of some of the properties connected with the inverse of the correlation matrix is provided and its use in the analysis of multivariate data is described.

In this paper, we provide an overview of recently developed methods for the analysis of multivariate data that do not necessarily emanate from a normal universe. Multivariate data occur naturally in the life sciences and in other research fields. When drawing inference, it is generally recommended to take the multivariate nature of the data into account, and not merely analyze each variable separately. Furthermore, it is often of major interest to select an appropriate set of important variables. We present contributions in three different, but closely related, research areas: first, a general approach to the comparison of mean vectors, which allows for profile analysis and tests of dimensionality; second, non-parametric and parametric methods for the comparison of independent samples of multivariate observations; and third, methods for the situation where the experimental units are observed repeatedly, for example, over time, and the main focus is on analyzing different time profiles when the number p of repeated observations per subject is larger than the number n of subjects.

&lt;p&gt;This thesis investigates three research problems which arise in multivariate data and censored regression. The first is the identification of outliers in multivariate data. The second is a dissimilarity measure for clustering purposes. The third is the diagnostics analysis for the Buckley-James method in censored regression. Outliers can be defined simply as an observation (or a subset of observations) that is isolated from the other observations in the data set. There are two main reasons that motivate people to find outliers; the first is the researcher's intention. The second is the effects of an outlier on analyses, i.e. the existence of outliers will affect means, variances and regression coefficients; they will also cause a bias or distortion of estimates; likewise, they will inflate the sums of squares and hence, false conclusions are likely to be created. Sometimes, the identification of outliers is the main objective of the analysis, and whether to remove the outliers or for them to be down-weighted prior to fitting a non-robust model. This thesis does not differentiate between the various justifications for outlier detection. The aim is to advise the analyst of observations that are considerably different from the majority. Note that the techniques for identification of outliers introduce in this thesis is applicable to a wide variety of settings. Those techniques are performed on large and small data sets. In this thesis, observations that are located far away from the remaining data are considered to be outliers. Additionally, it is noted that some techniques for the identification of outliers are available for finding clusters. There are two major challenges in clustering. The first is identifying clusters in high-dimensional data sets is a difficult task because of the curse of dimensionality. The second is a new dissimilarity measure is needed as some traditional distance functions cannot capture the pattern dissimilarity among the objects. This thesis deals with the latter challenge. This thesis introduces Influence Angle Cluster Approach (iaca) that may be used as a dissimilarity matrix and the author has managed to show that iaca successfully develops a cluster when it is used in partitioning clustering, even if the data set has mixed variables, i.e. interval and categorical variables. The iaca is developed based on the influence eigenstructure. The first two problems in this thesis deal with a complete data set. It is also interesting to study about the incomplete data set, i.e. censored data set. The term 'censored' is mostly used in biological science areas such as a survival analysis. Nowadays, researchers are interested in comparing the survival distribution of two samples. Even though this can be done by using the logrank test, this method cannot examine the effects of more than one variable at a time. This difficulty can easily be overcome by using the survival regression model. Examples of the survival regression model are the Cox model, Miller's model, the Buckely James model and the Koul- Susarla-Van Ryzin model. The Buckley James model's performance is comparable with the Cox model and the former performs best when compared both to the Miller model and the Koul-Susarla-Van Ryzin model. Previous comparison studies proved that the Buckley-James estimator is more stable and easier to explain to non-statisticians than the Cox model. Today, researchers are interested in using the Cox model instead of the Buckley-James model. This is because of the lack of function of Buckley-James model in the computer software and choices of diagnostics analysis. Currently, there are only a few diagnostics analyses for Buckley James model that exist. Therefore, this thesis proposes two new diagnostics analyses for the Buckley-James model. The first proposed diagnostics analysis is called renovated Cook's distance. This method produces comparable results with the previous findings. Nevertheless, this method cannot identify influential observations from the censored group. It can only detect influential observations from the uncensored group. This issue needs further investigation because of the possibility of censored points becoming influential cases in censored regression. Secondly, the local influence approach for the Buckley-James model is proposed. This thesis presents the local influence diagnostics of the Buckley-James model which consist of variance perturbation, response variable perturbation, censoring status perturbation, and independent variables perturbation. The proposed diagnostics improves and also challenge findings of the previous ones by taking into account both censored and uncensored data to have a possibility to become an influential observation.&lt;/p&gt;

Principal component analysis concerned with explaining the variance-covariance structure of a set of variables through a few linear combinations of these variables. To determine how many principal components should be considered, the eigenvalues should first be examined. Investigating whether the processing of numbers depend on the way the numbers were presented, i.e. whether the data could be reduced. Four variables (WordDiff, WordSame, ArabicDiff and ArabicSame) were used. Both covariate and correlation matrix were used to obtain the principal components and compare the results between them. In addition, canonical correlation was used to examine the correlation between the set of Word variables and the set of Arabic variables. To see the correlation between the Word variables and Arabic variables, observing the canonical correlation between the first Word canonical variable and the first Arabic variable is enough. Data was reduced into a single principal component (PC1) as more than 80% of the total variability was explained by this principal component.

Now a day's large datasets can be very effective in successful business decision making which includes tracking sales performance, analyzing the revenue streams, consumer preferences, competitor analysis and market trends and positioning. Large datasets also play a crucial role in driving innovations and advancing technology. Researchers can leverage publically large datasets to conduct various studies. Large datasets also provide the robust validations and this vast amount of data can provide more relevant recommendations and advertisements. In various fields like finance or healthcare the large datasets enables the better business decisions by the comprehensive data-driven insight, this can lead the better decision making and risk management and other healthcare interventions. Using large dataset, the machine learning models can be trained effectively, with the better accuracy and performance and can detect the complex patterns. When selecting a dataset for data visualizations it is necessary to ensure data quality, relevance to the business goals as well as data privacy. Exploratory data analysis (EDA) plays a vital role before finalizing the dataset because EDA can explore uncover patterns, trends, other visualization techniques like charts and dashboards for decision-making across various functional units. This study investigate the exploratory data analysis of Insta cart dataset includes product items, product departments, best-selling Aisles, most frequent order and most Reorder Products. Also what are the exploratory issues for future recommendation systems implementation? In this exploration we used the pandas and numpy for the purpose of the data manipulation, and data exploration.

Based on benchmarking various methods and analyzing multiple real scRNA-seq datasets, a computational platform/workflow and a set of tips for best practices are developed for analyzing causal interactions or relationships in single cells.

It is a common challenge for the geosciences to jointly model the uncertainty in continuous and categorical regionalised variables and to reproduce observed spatial correlation and complex relationships in realisations. The demand for computational efficiency in the case of high-dimensional data and large simulation domains has led practitioners to utilise approaches based on decorrelation/recorrelation and independent simulation. Among such approaches the method of min/max autocorrelation factors (MAF) has proven to be a practical technique for industrial purposes. This study presents a hybrid model for joint simulation of high-dimensional continuous and categorical variables. Continuous variables are transformed to Gaussian random functions (GRFs) via anamorphosis functions and categorical variables are obtained by truncating one or more GRFs based on the plurigaussian model. MAF factors are then derived from all GRFs. After independent simulation of MAF factors, different realisations of continuous and categorical variables are obtained via back-transformation of MAF factors followed by back-transformation for continuous and truncation for categorical variables, respectively. The proposed algorithm is illustrated through a case study.