Inference And Prediction In Large Dimensions
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| Author | : Denis Bosq |
| Publisher | : John Wiley & Sons |
| Total Pages | : 336 |
| Release | : 2008-03-11 |
| Genre | : Mathematics |
| ISBN | : 9780470724026 |
This book offers a predominantly theoretical coverage of statistical prediction, with some potential applications discussed, when data and/ or parameters belong to a large or infinite dimensional space. It develops the theory of statistical prediction, non-parametric estimation by adaptive projection – with applications to tests of fit and prediction, and theory of linear processes in function spaces with applications to prediction of continuous time processes. This work is in the Wiley-Dunod Series co-published between Dunod (www.dunod.com) and John Wiley and Sons, Ltd.
| Author | : Bradley Efron |
| Publisher | : |
| Total Pages | : 276 |
| Release | : 2010 |
| Genre | : |
| ISBN | : |
We live in a new age for statistical inference, where modern scientific technology such as microarrays and fMRI machines routinely produce thousands and sometimes millions of parallel data sets, each with its own estimation or testing problem. Doing thousands of problems at once is more than repeated application of classical methods. Taking an empirical Bayes approach, Bradley Efron, inventor of the bootstrap, shows how information accrues across problems in a way that combines Bayesian and frequentist ideas. Estimation, testing and prediction blend in this framework, producing opportunities for new methodologies of increased power. New difficulties also arise, easily leading to flawed inferences. This book takes a careful look at both the promise and pitfalls of large-scale statistical inference, with particular attention to false discovery rates, the most successful of the new statistical techniques. Emphasis is on the inferential ideas underlying technical developments, illustrated using a large number of real examples.
| Author | : Bradley Efron |
| Publisher | : Cambridge University Press |
| Total Pages | : |
| Release | : 2012-11-29 |
| Genre | : Mathematics |
| ISBN | : 1139492136 |
We live in a new age for statistical inference, where modern scientific technology such as microarrays and fMRI machines routinely produce thousands and sometimes millions of parallel data sets, each with its own estimation or testing problem. Doing thousands of problems at once is more than repeated application of classical methods. Taking an empirical Bayes approach, Bradley Efron, inventor of the bootstrap, shows how information accrues across problems in a way that combines Bayesian and frequentist ideas. Estimation, testing and prediction blend in this framework, producing opportunities for new methodologies of increased power. New difficulties also arise, easily leading to flawed inferences. This book takes a careful look at both the promise and pitfalls of large-scale statistical inference, with particular attention to false discovery rates, the most successful of the new statistical techniques. Emphasis is on the inferential ideas underlying technical developments, illustrated using a large number of real examples.
| Author | : Mohsen Pourahmadi |
| Publisher | : John Wiley & Sons |
| Total Pages | : 204 |
| Release | : 2013-05-28 |
| Genre | : Mathematics |
| ISBN | : 1118573668 |
Methods for estimating sparse and large covariance matrices Covariance and correlation matrices play fundamental roles in every aspect of the analysis of multivariate data collected from a variety of fields including business and economics, health care, engineering, and environmental and physical sciences. High-Dimensional Covariance Estimation provides accessible and comprehensive coverage of the classical and modern approaches for estimating covariance matrices as well as their applications to the rapidly developing areas lying at the intersection of statistics and machine learning. Recently, the classical sample covariance methodologies have been modified and improved upon to meet the needs of statisticians and researchers dealing with large correlated datasets. High-Dimensional Covariance Estimation focuses on the methodologies based on shrinkage, thresholding, and penalized likelihood with applications to Gaussian graphical models, prediction, and mean-variance portfolio management. The book relies heavily on regression-based ideas and interpretations to connect and unify many existing methods and algorithms for the task. High-Dimensional Covariance Estimation features chapters on: Data, Sparsity, and Regularization Regularizing the Eigenstructure Banding, Tapering, and Thresholding Covariance Matrices Sparse Gaussian Graphical Models Multivariate Regression The book is an ideal resource for researchers in statistics, mathematics, business and economics, computer sciences, and engineering, as well as a useful text or supplement for graduate-level courses in multivariate analysis, covariance estimation, statistical learning, and high-dimensional data analysis.
| Author | : Arend L. Voorman |
| Publisher | : |
| Total Pages | : 117 |
| Release | : 2014 |
| Genre | : |
| ISBN | : |
In many areas of biology, recent advances in technology have facilitated the measurement of large numbers of features, while the number of observations in a data set may remain relatively modest. In this setting, lasso regression and related procedures have been extensively studied for prediction, while the problem of inference is relatively less studied. Most inference in high dimensions is based on simple marginal associations between variables. However, a richer characterization of the associations between variables can be obtained by examining conditional relationships, which account for the joint behavior of the variables. Inference on conditional relationships is more difficult, because it requires one to specify how features are related to one another, to estimate these relationships, and to characterize the uncertainty in the estimation procedure. In Chapters 2 and 3, we explore a few methods for testing hypotheses about conditional relationships in the high-dimensional setting. In Chapter 4, we note some strong distributional assumptions implicit in many treatments of high-dimensional graphical models, and propose a modification which treats this issue.
| Author | : Natalia Markovich |
| Publisher | : John Wiley & Sons |
| Total Pages | : 336 |
| Release | : 2008-03-11 |
| Genre | : Mathematics |
| ISBN | : 9780470723593 |
Heavy-tailed distributions are typical for phenomena in complex multi-component systems such as biometry, economics, ecological systems, sociology, web access statistics, internet traffic, biblio-metrics, finance and business. The analysis of such distributions requires special methods of estimation due to their specific features. These are not only the slow decay to zero of the tail, but also the violation of Cramer’s condition, possible non-existence of some moments, and sparse observations in the tail of the distribution. The book focuses on the methods of statistical analysis of heavy-tailed independent identically distributed random variables by empirical samples of moderate sizes. It provides a detailed survey of classical results and recent developments in the theory of nonparametric estimation of the probability density function, the tail index, the hazard rate and the renewal function. Both asymptotical results, for example convergence rates of the estimates, and results for the samples of moderate sizes supported by Monte-Carlo investigation, are considered. The text is illustrated by the application of the considered methodologies to real data of web traffic measurements.
| Author | : Deborah G. Mayo |
| Publisher | : Cambridge University Press |
| Total Pages | : 503 |
| Release | : 2018-09-20 |
| Genre | : Mathematics |
| ISBN | : 1108563309 |
Mounting failures of replication in social and biological sciences give a new urgency to critically appraising proposed reforms. This book pulls back the cover on disagreements between experts charged with restoring integrity to science. It denies two pervasive views of the role of probability in inference: to assign degrees of belief, and to control error rates in a long run. If statistical consumers are unaware of assumptions behind rival evidence reforms, they can't scrutinize the consequences that affect them (in personalized medicine, psychology, etc.). The book sets sail with a simple tool: if little has been done to rule out flaws in inferring a claim, then it has not passed a severe test. Many methods advocated by data experts do not stand up to severe scrutiny and are in tension with successful strategies for blocking or accounting for cherry picking and selective reporting. Through a series of excursions and exhibits, the philosophy and history of inductive inference come alive. Philosophical tools are put to work to solve problems about science and pseudoscience, induction and falsification.
| Author | : Shao-Lun Huang |
| Publisher | : Now Publishers |
| Total Pages | : 0 |
| Release | : 2024-02-05 |
| Genre | : Computers |
| ISBN | : 9781638281764 |
In many contemporary and emerging applications of machine learning and statistical inference, the phenomena of interest are characterized by variables defined over large alphabets. This increasing size of both the data and the number of inferences, and the limited available training data means there is a need to understand which inference tasks can be most effectively carried out, and, in turn, what features of the data are most relevant to them. In this monograph, the authors develop the idea of extracting "universally good" features, and establish that diverse notions of such universality lead to precisely the same features. The information-theoretic approach used results in a local information geometric analysis that facilitates their computation in a host of applications. The authors provide a comprehensive treatment that guides the reader through the basic principles to the advanced techniques including many new results. They emphasize a development from first-principles together with common, unifying terminology and notation, and pointers to the rich embodying literature, both historical and contemporary. Written for students and researchers, this monograph is a complete treatise on the information theoretic treatment of a recognized and current problem in machine learning and statistical inference.
| Author | : David W. Scott |
| Publisher | : John Wiley & Sons |
| Total Pages | : 384 |
| Release | : 2015-03-12 |
| Genre | : Mathematics |
| ISBN | : 1118575539 |
Clarifies modern data analysis through nonparametric density estimation for a complete working knowledge of the theory and methods Featuring a thoroughly revised presentation, Multivariate Density Estimation: Theory, Practice, and Visualization, Second Edition maintains an intuitive approach to the underlying methodology and supporting theory of density estimation. Including new material and updated research in each chapter, the Second Edition presents additional clarification of theoretical opportunities, new algorithms, and up-to-date coverage of the unique challenges presented in the field of data analysis. The new edition focuses on the various density estimation techniques and methods that can be used in the field of big data. Defining optimal nonparametric estimators, the Second Edition demonstrates the density estimation tools to use when dealing with various multivariate structures in univariate, bivariate, trivariate, and quadrivariate data analysis. Continuing to illustrate the major concepts in the context of the classical histogram, Multivariate Density Estimation: Theory, Practice, and Visualization, Second Edition also features: Over 150 updated figures to clarify theoretical results and to show analyses of real data sets An updated presentation of graphic visualization using computer software such as R A clear discussion of selections of important research during the past decade, including mixture estimation, robust parametric modeling algorithms, and clustering More than 130 problems to help readers reinforce the main concepts and ideas presented Boxed theorems and results allowing easy identification of crucial ideas Figures in color in the digital versions of the book A website with related data sets Multivariate Density Estimation: Theory, Practice, and Visualization, Second Edition is an ideal reference for theoretical and applied statisticians, practicing engineers, as well as readers interested in the theoretical aspects of nonparametric estimation and the application of these methods to multivariate data. The Second Edition is also useful as a textbook for introductory courses in kernel statistics, smoothing, advanced computational statistics, and general forms of statistical distributions.
| Author | : Vijay K. Rohatgi |
| Publisher | : John Wiley & Sons |
| Total Pages | : 722 |
| Release | : 2015-09-08 |
| Genre | : Mathematics |
| ISBN | : 111879964X |
A well-balanced introduction to probability theory and mathematical statistics Featuring updated material, An Introduction to Probability and Statistics, Third Edition remains a solid overview to probability theory and mathematical statistics. Divided intothree parts, the Third Edition begins by presenting the fundamentals and foundationsof probability. The second part addresses statistical inference, and the remainingchapters focus on special topics. An Introduction to Probability and Statistics, Third Edition includes: A new section on regression analysis to include multiple regression, logistic regression, and Poisson regression A reorganized chapter on large sample theory to emphasize the growing role of asymptotic statistics Additional topical coverage on bootstrapping, estimation procedures, and resampling Discussions on invariance, ancillary statistics, conjugate prior distributions, and invariant confidence intervals Over 550 problems and answers to most problems, as well as 350 worked out examples and 200 remarks Numerous figures to further illustrate examples and proofs throughout An Introduction to Probability and Statistics, Third Edition is an ideal reference and resource for scientists and engineers in the fields of statistics, mathematics, physics, industrial management, and engineering. The book is also an excellent text for upper-undergraduate and graduate-level students majoring in probability and statistics.
