Download or read book The Energy of Data and Distance Correlation written by Gabor J. Szekely and published by CRC Press. This book was released on 2023-02-15 with total page 444 pages. Available in PDF, EPUB and Kindle. Book excerpt: Energy distance is a statistical distance between the distributions of random vectors, which characterizes equality of distributions. The name energy derives from Newton's gravitational potential energy, and there is an elegant relation to the notion of potential energy between statistical observations. Energy statistics are functions of distances between statistical observations in metric spaces. The authors hope this book will spark the interest of most statisticians who so far have not explored E-statistics and would like to apply these new methods using R. The Energy of Data and Distance Correlation is intended for teachers and students looking for dedicated material on energy statistics, but can serve as a supplement to a wide range of courses and areas, such as Monte Carlo methods, U-statistics or V-statistics, measures of multivariate dependence, goodness-of-fit tests, nonparametric methods and distance based methods. •E-statistics provides powerful methods to deal with problems in multivariate inference and analysis. •Methods are implemented in R, and readers can immediately apply them using the freely available energy package for R. •The proposed book will provide an overview of the existing state-of-the-art in development of energy statistics and an overview of applications. •Background and literature review is valuable for anyone considering further research or application in energy statistics.
Download or read book The Energy of Data and Distance Correlation written by Gabor J. Szekely and published by CRC Press. This book was released on 2023-06-30 with total page 467 pages. Available in PDF, EPUB and Kindle. Book excerpt: Energy distance is a statistical distance between the distributions of random vectors, which characterizes equality of distributions. The name energy derives from Newton's gravitational potential energy, and there is an elegant relation to the notion of potential energy between statistical observations. Energy statistics are functions of distances between statistical observations in metric spaces. The authors hope this book will spark the interest of most statisticians who so far have not explored E-statistics and would like to apply these new methods using R. The Energy of Data and Distance Correlation is intended for teachers and students looking for dedicated material on energy statistics, but can serve as a supplement to a wide range of courses and areas, such as Monte Carlo methods, U-statistics or V-statistics, measures of multivariate dependence, goodness-of-fit tests, nonparametric methods and distance based methods. •E-statistics provides powerful methods to deal with problems in multivariate inference and analysis. •Methods are implemented in R, and readers can immediately apply them using the freely available energy package for R. •The proposed book will provide an overview of the existing state-of-the-art in development of energy statistics and an overview of applications. •Background and literature review is valuable for anyone considering further research or application in energy statistics.
Download or read book The Energy of Data written by Gábor J. Székely and published by . This book was released on 2017 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: The energy of data is the value of a real function of distances between data in metric spaces. The name energy derives from Newton's gravitational potential energy, which is also a function of distances between physical objects. One of the advantages of working with energy functions (energy statistics) is that even if the data are complex objects, such as functions or graphs, we can use their real-valued distances for inference. Other advantages are illustrated and discussed in this review. Concrete examples include energy testing for normality, energy clustering, and distance correlation. Applications include genome studies, brain studies, and astrophysics. The direct connection between energy and mind/observations/data in this review is a counterpart of the equivalence of energy and matter/mass in Einstein's E=mc.
Download or read book Energy Distance Correlation with Extended Bayesian Information Criteria for Feature Selection in High Dimensional Models written by Isaac Xoese Ocloo and published by . This book was released on 2021 with total page 61 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this research, we investigate the sequential lasso method for feature selection in sparse high dimensional linear models. It was recently proposed by Luo and Chen (2014). In this project, wepropose a new method by introducing the energy distance correlation by Szekely et al. (2007) to replace the ordinary correlation in Luo and Chen's algorithm. We continue to adopt the extended Bayesian Information Criteria as the stopping criteria in the computing algorithm. The advantageof energy distance correlation is that it is able to detect linear and non-linear association betweentwo variables, while the ordinary correlation can detect only linear part of association between twovariables. As a result, it appears that the new method is shown to be more powerful than Luo andChen's method for feature selections. This is demonstrated by simulation studies and illustrated by two real-life examples. It is shown that the proposed new algorithm is also selection consistent. For the first part of our research we examine through simulations the model size selectionby Adaptive Lasso and SCAD after a sure screening method proposed by Li et al. (2012) usingdistance correlation is applied to the data first. We observe that the average model size selectedwas quite high. In the second part we describe the new sequential variable selection method which we call energy distance correlation with extended Bayesian Information Criteria (Edc+EBIC). At each stageof the sequential procedure we maximize the energy distance correlation between the response andeach of the predictor variables. This maximization is done such that if a variable is selected in theprevious stage, it's contribution to the response is removed so that it won't have a chance of beingselected again. The active set of selected variables is updated once a variable is selected and theEBIC of the set is calculated. The process stops if the EBIC for the current active set is greater thanthe EBIC of the previous active set. We compare the performance of Edc+EBIC with sequentialLasso, Adaptive Lasso, SCAD and SIS+SCAD. We observed that our proposed method on averagehas a positive discovery rate close to 100%, a low false discovery rate and an average model sizeas expected in our simulation set-up.
Download or read book Risk Reliability and Safety Innovating Theory and Practice written by Lesley Walls and published by CRC Press. This book was released on 2016-11-25 with total page 2983 pages. Available in PDF, EPUB and Kindle. Book excerpt: Risk, Reliability and Safety contains papers describing innovations in theory and practice contributed to the scientific programme of the European Safety and Reliability conference (ESREL 2016), held at the University of Strathclyde in Glasgow, Scotland (25—29 September 2016). Authors include scientists, academics, practitioners, regulators and other key individuals with expertise and experience relevant to specific areas. Papers include domain specific applications as well as general modelling methods. Papers cover evaluation of contemporary solutions, exploration of future challenges, and exposition of concepts, methods and processes. Topics include human factors, occupational health and safety, dynamic and systems reliability modelling, maintenance optimisation, uncertainty analysis, resilience assessment, risk and crisis management.
Download or read book 1999 European Wind Energy Conference written by E.L. Petersen and published by Routledge. This book was released on 2014-01-02 with total page 1281 pages. Available in PDF, EPUB and Kindle. Book excerpt: The 1999 European Wind Energy Conference and Exhibition was organized to review progress, and present and discuss the wind energy business, technology and science for the future. The Proceedings contain a selection of over 300 papers from the conference. They represent a significant update to the understanding of this increasingly important field of energy generation and cover a full range of topics.
Download or read book Local Distance Correlation written by Walaa Ahmed Hamdi and published by . This book was released on 2020 with total page 117 pages. Available in PDF, EPUB and Kindle. Book excerpt: Distance correlation is a measure of the relationship between random vectors in arbitrary dimension. A sample distance covariance can be formulated in both an unbiased estimator and a biased estimator of distance covariance, where distance correlation is defined as the normalized coefficient of distance covariance. The jackknife empirical likelihood for a U-statistic by Jing, Yuan, and Zhou (2009) can be applied to a distance correlation since the empirical likelihood method fails in nonlinear statistics. A Wilks' theorem for jackknife empirical likelihood is shown to hold for distance correlation. This research shows how to construct a confidence interval for distance correlation based on jackknife empirical likelihood for a U-statistic, where the sample distance covariance can be represented as a U-statistic. In comparing coverage probabilities of confidence intervals for distance correlation based on jackknife empirical likelihood and bootstrap method, coverage probabilities for the jackknife empirical likelihood show more accuracy. We propose the estimation and the visualization of local distance correlation by using a local version of the jackknife empirical likelihood. The kernel density functional estimation is used to construct the jackknife empirical likelihood locally. The bandwidth selection for kernel function should minimize the distance between the true density and estimated density. Local distance correlation has the property that it equals zero in the neighborhood of each point if and only if the two variables are independent in that neighborhood. The estimation and visualization of local distance correlation are shown as accurate to capture the local dependence when compared with the local Gaussian correlation in simulation studies and real examples.
Download or read book Wind Energy for the Next Millennium written by E. L. Petersen and published by Earthscan. This book was released on 1999 with total page 1290 pages. Available in PDF, EPUB and Kindle. Book excerpt: First Published in 1999. Routledge is an imprint of Taylor & Francis, an informa company.
Download or read book Spurious Correlations written by Tyler Vigen and published by Hachette Books. This book was released on 2015-05-12 with total page 303 pages. Available in PDF, EPUB and Kindle. Book excerpt: "Spurious Correlations ... is the most fun you'll ever have with graphs." -- Bustle Military intelligence analyst and Harvard Law student Tyler Vigen illustrates the golden rule that "correlation does not equal causation" through hilarious graphs inspired by his viral website. Is there a correlation between Nic Cage films and swimming pool accidents? What about beef consumption and people getting struck by lightning? Absolutely not. But that hasn't stopped millions of people from going to tylervigen.com and asking, "Wait, what?" Vigen has designed software that scours enormous data sets to find unlikely statistical correlations. He began pulling the funniest ones for his website and has since gained millions of views, hundreds of thousands of likes, and tons of media coverage. Subversive and clever, Spurious Correlations is geek humor at its finest, nailing our obsession with data and conspiracy theory.
Download or read book N distances and Their Applications written by Lev B. Klebanov and published by Karolinum Press, Charles University. This book was released on 2006-04 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book focuses on probability metrics suitable for the characterization of random variables in Hilbert or Banach space. It provides details of various stochastic processes, such as testing non-deterministic statistical hypotheses, characterization of probability distribution or constructing multidimensional test for two selections. The book is published in the English language.
Download or read book Distance Correlation and Multivariate Extremes written by and published by . This book was released on 2016 with total page 80 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Long Distance Energy Correlations in Random Media written by Daniel Zwillinger and published by . This book was released on 1983 with total page 406 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Statistical Computing with R written by Maria L. Rizzo and published by CRC Press. This book was released on 2007-11-15 with total page 412 pages. Available in PDF, EPUB and Kindle. Book excerpt: Computational statistics and statistical computing are two areas that employ computational, graphical, and numerical approaches to solve statistical problems, making the versatile R language an ideal computing environment for these fields. One of the first books on these topics to feature R, Statistical Computing with R covers the traditiona
Download or read book Foundations of Data Science written by Avrim Blum and published by Cambridge University Press. This book was released on 2020-01-23 with total page 433 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides an introduction to the mathematical and algorithmic foundations of data science, including machine learning, high-dimensional geometry, and analysis of large networks. Topics include the counterintuitive nature of data in high dimensions, important linear algebraic techniques such as singular value decomposition, the theory of random walks and Markov chains, the fundamentals of and important algorithms for machine learning, algorithms and analysis for clustering, probabilistic models for large networks, representation learning including topic modelling and non-negative matrix factorization, wavelets and compressed sensing. Important probabilistic techniques are developed including the law of large numbers, tail inequalities, analysis of random projections, generalization guarantees in machine learning, and moment methods for analysis of phase transitions in large random graphs. Additionally, important structural and complexity measures are discussed such as matrix norms and VC-dimension. This book is suitable for both undergraduate and graduate courses in the design and analysis of algorithms for data.
Download or read book Robust Correlation written by Georgy L. Shevlyakov and published by John Wiley & Sons. This book was released on 2016-09-08 with total page 352 pages. Available in PDF, EPUB and Kindle. Book excerpt: This bookpresents material on both the analysis of the classical concepts of correlation and on the development of their robust versions, as well as discussing the related concepts of correlation matrices, partial correlation, canonical correlation, rank correlations, with the corresponding robust and non-robust estimation procedures. Every chapter contains a set of examples with simulated and real-life data. Key features: Makes modern and robust correlation methods readily available and understandable to practitioners, specialists, and consultants working in various fields. Focuses on implementation of methodology and application of robust correlation with R. Introduces the main approaches in robust statistics, such as Huber’s minimax approach and Hampel’s approach based on influence functions. Explores various robust estimates of the correlation coefficient including the minimax variance and bias estimates as well as the most B- and V-robust estimates. Contains applications of robust correlation methods to exploratory data analysis, multivariate statistics, statistics of time series, and to real-life data. Includes an accompanying website featuring computer code and datasets Features exercises and examples throughout the text using both small and large data sets. Theoretical and applied statisticians, specialists in multivariate statistics, robust statistics, robust time series analysis, data analysis and signal processing will benefit from this book. Practitioners who use correlation based methods in their work as well as postgraduate students in statistics will also find this book useful.
Download or read book Statistical Power Analysis for the Behavioral Sciences written by Jacob Cohen and published by Routledge. This book was released on 2013-05-13 with total page 625 pages. Available in PDF, EPUB and Kindle. Book excerpt: Statistical Power Analysis is a nontechnical guide to power analysis in research planning that provides users of applied statistics with the tools they need for more effective analysis. The Second Edition includes: * a chapter covering power analysis in set correlation and multivariate methods; * a chapter considering effect size, psychometric reliability, and the efficacy of "qualifying" dependent variables and; * expanded power and sample size tables for multiple regression/correlation.
Download or read book Forum on Turbulent Flows written by and published by . This book was released on 1993 with total page 212 pages. Available in PDF, EPUB and Kindle. Book excerpt:
