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Book
xvi, 396 p. : ill. ; 24 cm.
  • Preface to the second edition.- Preface to the first edition.- Introduction.- LDP for Finite Dimensional Space.- Applications - The Finite Dimensional Case.- General Principles.- Sample Path Large Deviations.- The LDP for Abstract Empirical Measures.- Applications of Empirical Measures LDP.- Appendices.- Bibliography.- General Conventions.- Index of Notation.- Index.
  • (source: Nielsen Book Data)9783642033100 20160527
dx.doi.org SpringerLink
Science Library (Li and Ma)
MATH-234-01, STATS-300C-01, STATS-374-01
Book
xii, 263 p. : ill. (some col.) ; 24 cm.
  • Introduction and foreword-- 1. Empirical Bayes and the James-Stein estimator-- 2. Large-scale hypothesis testing-- 3. Significance testing algorithms-- 4. False discovery rate control-- 5. Local false discovery rates-- 6. Theoretical, permutation and empirical null distributions-- 7. Estimation accuracy-- 8. Correlation questions-- 9. Sets of cases (enrichment)-- 10. Combination, relevance, and comparability-- 11. Prediction and effect size estimation-- A. Exponential families-- B. Programs and data sets-- Bibliography-- Index.
  • (source: Nielsen Book Data)9780521192491 20160604
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.
(source: Nielsen Book Data)9780521192491 20160604
Science Library (Li and Ma)
STATS-300C-01
Book
xvii, 448 p. : ill. ; 24 cm.
  • Preface.- Part I. Gaussian Processes. Gaussian Fields. Gaussian Inequalities. Orthogonal Expansions. Excursion Probabilities. Stationary Fields.- Parat II. Geometry. Integral Geometry. Differential Geometry. Piecewise Smooth Manifolds. Critical Point Theory. Volume of Tubes.- Part III. The Geometry of Random Fields. Random Fields on Euclidean Spaces. Random Fields on Manifolds. Mean Intrinsic Volumes. Excursion Probabilities for Smooth Fields. Non-Gaussian Geometry.- References.- Index.
  • (source: Nielsen Book Data)9780387481128 20160528
This monograph is devoted to a completely new approach to geometric problems arising in the study of random fields. The groundbreaking material in Part III, for which the background is carefully prepared in Parts I and II, is of both theoretical and practical importance, and striking in the way in which problems arising in geometry and probability are beautifully intertwined. The three parts to the monograph are quite distinct. Part I presents a user-friendly yet comprehensive background to the general theory of Gaussian random fields, treating classical topics such as continuity and boundedness, entropy and majorizing measures, Borell and Slepian inequalities. Part II gives a quick review of geometry, both integral and Riemannian, to provide the reader with the material needed for Part III, and to give some new results and new proofs of known results along the way. Topics such as Crofton formulae, curvature measures for stratified manifolds, critical point theory, and tube formulae are covered. In fact, this is the only concise, self-contained treatment of all of the above topics, which are necessary for the study of random fields. The new approach in Part III is devoted to the geometry of excursion sets of random fields and the related Euler characteristic approach to extremal probabilities. "Random Fields and Geometry" will be useful for probabilists and statisticians, and for theoretical and applied mathematicians who wish to learn about new relationships between geometry and probability. It will be helpful for graduate students in a classroom setting, or for self-study. Finally, this text will serve as a basic reference for all those interested in the companion volume of the applications of the theory. These applications, to appear in a forthcoming volume, will cover areas as widespread as brain imaging, physical oceanography, and astrophysics.
(source: Nielsen Book Data)9780387481128 20160528
Science Library (Li and Ma)
STATS-300C-01