Series: Springer Texts in Statistics, Vol.
2011, XVI, 641 p. 55 illus., Hardcover
ISBN: 978-1-4419-9633-6
Due: June 29, 2011
Unification of probability, statistics, and machine learning tools provides a complete background for teaching and future research inmultiple areas
Lucid and encyclopedic coverage allows the user to find and conceptually understand numerous topics by using a single source
1225 worked out examples and exercises provide essential skills in problem solving and help in self-study
This book provides a versatile and lucid treatment of classic as well as modern probability theory, while integrating them with core topics in statistical theory and also some key tools in machine learning. It is written in an extremely accessible style, with elaborate motivating discussions and numerous worked out examples and exercises. The book has 20 chapters on a wide range of topics, 423 worked out examples, and 808 exercises. It is unique in its unification of probability and statistics, its coverage and its superb exercise sets, detailed bibliography, and in its substantive treatment of many topics of current importance.
This book can be used as a text for a year long graduate course in statistics, computer science, or mathematics, for self-study, and as an invaluable research reference on probabiliity and its applications. Particularly worth mentioning are the treatments of distribution theory, asymptotics, simulation and Markov Chain Monte Carlo, Markov chains and martingales, Gaussian processes, VC theory, probability metrics, large deviations, bootstrap, the EM algorithm, confidence intervals, maximum likelihood and Bayes estimates, exponential families, kernels, and Hilbert spaces, and a self contained complete review of univariate probability.
Content Level ≫ Upper undergraduate
Keywords ≫ Asymptotics - Boot Strap - Machine Learning - Markov Chain Monte Carlo - Proabability models
Related subjects ≫ Bioinformatics - Probability Theory and Stochastic Processes - Statistical Theory and Methods - Theoretical Computer Science
Chapter 1. Review of Univariate Probability.- Chapter 2. Multivariate Discrete Distributions.- Chapter 3. Multidimensional Densities.- Chapter 4. Advance Distribution Theory.- Chapter 5. Multivariate Normal and Related Distributions.- Chapter 6. Finite Sample Theory of Order Statistics and Extremes.- Chapter 7. Essential Asymptotics and Applications.- Chapter 8. Characteristic Functions and Applications.- Chapter 9. Asymptotics of Extremes and Order Statistics.- Chapter 10. Markov Chains and Applications.- Chapter 11. Random Walks.- Chapter 12. Brownian Motion and Gaussian Processes.- Chapter 13. Posson Processes and Applications.- Chapter 14. Discrete Time Martingales and Concentration Inequalities.- Chapter 15. Probability Metrics.- Chapter 16. Empirical Processes and VC Theory.- Chapter 17. Large Deviations.- Chapter 18. The Exponential Family and Statistical Applications.- Chapter 19. Simulation and Markov Chain Monte Carlo.- Chapter 20. Useful Tools for Statistics and Machine Learning.- Appendix A. Symbols, Useful Formulas, and Normal Table.
Series: Use R
2011, X, 273 p. 92 illus., Softcover
ISBN: 978-1-4419-9649-7
Due: June 29, 2011
.Comprehensively covers a wide variety of multivariate analysis techniques using R
Covers the use of Rs graphical capabilities for interpretation of multivariate data
Provides extensive examples of R code used to apply the multivariate techniques to multivariate data
The majority of data sets collected by researchers in all disciplines are multivariate, meaning that several measurements, observations, or recordings are taken on each of the units in the data set. These units might be human subjects, archaeological artifacts, countries, or a vast variety of other things. In a few cases, it may be sensible to isolate each variable and study it separately, but in most instances all the variables need to be examined simultaneously in order to fully grasp the structure and key features of the data. For this purpose, one or another method of multivariate analysis might be helpful, and it is with such methods that this book is largely concerned. Multivariate analysis includes methods both for describing and exploring such data and for making formal inferences about them. The aim of all the techniques is, in general sense, to display or extract the signal in the data in the presence of noise and to find out what the data show us in the midst of their apparent chaos.
An Introduction to Applied Multivariate Analysis with R explores the correct application of these methods so as to extract as much information as possible from the data at hand, particularly as some type of graphical representation, via the R software. Throughout the book, the authors give many examples of R code used to apply the multivariate techniques to multivariate data.
Content Level ≫ Professional/practitioner
Keywords ≫ Multivariate Analysis
Related subjects ≫ Statistical Theory and Methods
Multivariate data and multivariate analysis.- Looking at multivariate data: visualization.- Principal components analysis.- Multidimensional scaling.- Exploratory factor analysis.- Cluster analysis.- Confirmatory factor analysis and structural equation models.- The analysis of repeated measures data.-
Series: Springer Series in Statistics
2011, L, 644 p. 75 illus., Hardcover
ISBN: 978-1-4419-9781-4
Due: July 13, 2011
Establishes causal inference methodology that incorporates the benefits of machine learning with statistical inference
Presentation combines accessibility with the method's rigorous grounding in statistical theory
Demonstrates targeted learning in epidemiological, medical, and genomic experimental and observational studies that include informative dropout, missingness, time-dependent confounding, and case-control sampling
The statistics profession is at a unique point in history. The need for valid statistical tools is greater than ever; data sets are massive, often measuring hundreds of thousands of measurements for a single subject. The field is ready to move towards clear objective benchmarks under which tools can be evaluated. Targeted learning allows (1) the full generalization and utilization of cross-validation as an estimator selection tool so that the subjective choices made by humans are now made by the machine, and (2) targeting the fitting of the probability distribution of the data toward the target parameter representing the scientific question of interest.
This book is aimed at both statisticians and applied researchers interested in causal inference and general effect estimation for observational and experimental data. Part I is an accessible introduction to super learning and the targeted maximum likelihood estimator, including related concepts necessary to understand and apply these methods. Parts II-IX handle complex data structures and topics applied researchers will immediately recognize from their own research, including time-to-event outcomes, direct and indirect effects, positivity violations, case-control studies, censored data, longitudinal data, and genomic studies.
Content Level ≫ Research
Keywords ≫ Causal inference
Related subjects ≫ Life Sciences, Medicine & Health - Public Health - Statistical Theory and Methods
Models, Inference, and Truth - The Open Problem - Defining the Model and Parameter - Super Learning - Introduction to TMLE - Understanding TMLE - Why TMLE? - Bounded Continuous Outcomes - Direct Effects and Effect Among the Treated - Marginal Structural Models - Positivity - Robust Analysis of RCTs Using Generalized Linear Models - Targeted ANCOVA Estimator in RCTs - Independent Case-Control Studies - Why Match? Matched Case-Control Studies - Nested Case-Control Risk Score Prediction - Super Learning for Right-Censored Data - RCTs with Time-to-Event Outcomes - RCTs with Time-to-Event Outcomes and Effect Modification Parameters - C-TMLE of an Additive Point Treatment Effect - C-TMLE for Time-to-Event Outcomes - Propensity-Score-Based Estimators and C-TMLE - Targeted Methods for Biomarker Discovery - Finding Quantitative Trait Loci Genes - Case Study: Longitudinal HIV Cohort Data - Probability of Success of an In Vitro Fertilization Program - Individualized Antiretroviral Initiation Rules - Cross-Validated Targeted Minimum-Loss-Based Estimation - Targeted Bayesian Learning - TMLE in Adaptive Group Sequential Covariate Adjusted RCTs - Foundations of TMLE - Introduction to R Code Implementation.-
2012, XIII, 393 p. 66 illus., 1 in color., Softcover
ISBN: 978-88-470-1940-9
Due: October 28, 2011
The book provides an introduction to Differential Geometry of Curves and Surfaces. The theory of curves starts with a discussion of possible definitions of the concept of curve, proving in particular the classification of 1-dimensional manifolds. We then present the classical local theory of parametrized plane and space curves (curves in n-dimensional space are discussed in the complementary material): curvature, torsion, Frenet’s formulas and the fundamental theorem of the local theory of curves. Then, after a self-contained presentation of degree theory for continuous self-maps of the circumference, we study the global theory of plane curves, introducing winding and rotation numbers, and proving the Jordan curve theorem for curves of class C2, and Hopf theorem on the rotation number of closed simple curves. The local theory of surfaces begins with a comparison of the concept of parametrized (i.e., immersed) surface with the concept of regular (i.e., embedded) surface. We then develop the basic differential geometry of surfaces in R3: definitions, examples, differentiable maps and functions, tangent vectors (presented both as vectors tangent to curves in the surface and as derivations on germs of differentiable functions; we shall consistently use both approaches in the whole book) and orientation. Next we study the several notions of curvature on a surface, stressing both the geometrical meaning of the objects introduced and the algebraic/analytical methods needed to study them via the Gauss map, up to the proof of Gauss’ Teorema Egregium. Then we introduce vector fields on a surface (flow, first integrals, integral curves) and geodesics (definition, basic properties, geodesic curvature, and, in the complementary material, a full proof of minimizing properties of geodesics and of the Hopf-Rinow theorem for surfaces). Then we shall present a proof of the celebrated Gauss-Bonnet theorem, both in its local and in its global form, using basic properties (fully proved in the complementary material) of triangulations of surfaces. As an application, we shall prove the Poincare-Hopf theorem on zeroes of vector fields. Finally, the last chapter will be devoted to several important results on the global theory of surfaces, like for instance the characterization of surfaces with constant Gaussian curvature, and the orientability of compact surfaces in R3.
Content Level ≫ Research
Related subjects ≫ Geometry & Topology - Image Processing - Mathematics - Numerical and Computational Mathematics