Let's Estimate


Book Description

Partying dinos explain estimation in this entertaining introduction by a tried-and-true team of fun math book creators. How much pizza do you need for a dinosaur party? If you don't know exactly, you have to estimate! This lively introduction to the mathematical concept of estimation is straightforward and fun. With brilliant clarity, David A. Adler explains what an estimate is and the difference between estimating and rounding. Edward Miller's colorful and energetic artwork offers the perfect accompaniment to concise, engaging text. Filled with graspable examples and simple explanations, Let's Estimate will have kids estimating like pros!




Let's Estimate


Book Description

Partying dinos explain estimation in this entertaining introduction by a tried-and-true team of fun math book creators. How much pizza do you need for a dinosaur party? If you don't know exactly, you have to estimate! This lively introduction to the mathematical concept of estimation is straightforward and fun. With brilliant clarity, David A. Adler explains what an estimate is and the difference between estimating and rounding. Edward Miller's colorful and energetic artwork offers the perfect accompaniment to concise, engaging text. Filled with graspable examples and simple explanations, Let's Estimate will have kids estimating like pros!




Function Estimates


Book Description

This volume collects together papers presented at the 1985 Conference in Function Estimation held at Humboldt State University. The papers focus especially on various types of spline estimations and convolution problems. The use of estimation and approximation methods as applied to geophysics, numerical analysis, and nonparametric statistics was a special feature of this conference.




Introduction to Probability


Book Description

Developed from celebrated Harvard statistics lectures, Introduction to Probability provides essential language and tools for understanding statistics, randomness, and uncertainty. The book explores a wide variety of applications and examples, ranging from coincidences and paradoxes to Google PageRank and Markov chain Monte Carlo (MCMC). Additional application areas explored include genetics, medicine, computer science, and information theory. The print book version includes a code that provides free access to an eBook version. The authors present the material in an accessible style and motivate concepts using real-world examples. Throughout, they use stories to uncover connections between the fundamental distributions in statistics and conditioning to reduce complicated problems to manageable pieces. The book includes many intuitive explanations, diagrams, and practice problems. Each chapter ends with a section showing how to perform relevant simulations and calculations in R, a free statistical software environment.




Estimating How the Macroeconomy Works


Book Description

Macroeconomics tries to describe and explain the economywide movement of prices, output, and unemployment. The field has been sharply divided among various schools, including Keynesian, monetarist, new classical, and others. It has also been split between theorists and empiricists. Ray Fair is a resolute empiricist, developing and refining methods for testing theories and models. The field cannot advance without the discipline of testing how well the models approximate the data. Using a multicountry econometric model, he examines several important questions, including what causes inflation, how monetary authorities behave and what are their stabilization limits, how large is the wealth effect on aggregate consumption, whether European monetary policy has been too restrictive, and how large are the stabilization costs to Europe of adopting the euro. He finds, among other things, little evidence for the rational expectations hypothesis and for the so-called non-accelerating inflation rate of unemployment (NAIRU) hypothesis. He also shows that the U.S. economy in the last half of the 1990s was not a new age economy.




Random Fields Estimation


Book Description

This book contains a novel theory of random fields estimation of Wiener type, developed originally by the author and presented here. No assumption about the Gaussian or Markovian nature of the fields are made. The theory, constructed entirely within the framework of covariance theory, is based on a detailed analytical study of a new class of multidimensional integral equations basic in estimation theory.This book is suitable for graduate courses in random fields estimation. It can also be used in courses in functional analysis, numerical analysis, integral equations, and scattering theory.




Difference Methods for Singular Perturbation Problems


Book Description

Difference Methods for Singular Perturbation Problems focuses on the development of robust difference schemes for wide classes of boundary value problems. It justifies the ε-uniform convergence of these schemes and surveys the latest approaches important for further progress in numerical methods. The first part of the book e




Strichartz Estimates and the Cauchy Problem for the Gravity Water Waves Equations


Book Description

This memoir is devoted to the proof of a well-posedness result for the gravity water waves equations, in arbitrary dimension and in fluid domains with general bottoms, when the initial velocity field is not necessarily Lipschitz. Moreover, for two-dimensional waves, the authors consider solutions such that the curvature of the initial free surface does not belong to L2. The proof is entirely based on the Eulerian formulation of the water waves equations, using microlocal analysis to obtain sharp Sobolev and Hölder estimates. The authors first prove tame estimates in Sobolev spaces depending linearly on Hölder norms and then use the dispersive properties of the water-waves system, namely Strichartz estimates, to control these Hölder norms.




Cellular Automata and Groups


Book Description

This unique book provides a self-contained exposition of the theory of cellular automata on groups and explores its deep connections with recent developments in geometric and combinatorial group theory, amenability, symbolic dynamics, the algebraic theory of group rings, and other branches of mathematics and theoretical computer science. The topics treated include the Garden of Eden theorem for amenable groups, the Gromov–Weiss surjunctivity theorem, and the solution of the Kaplansky conjecture on the stable finiteness of group rings for sofic groups. Entirely self-contained and now in its second edition, the volume includes 10 appendices and more than 600 exercises, the solutions of which are presented in the companion book Exercises in Cellular Automata and Groups (2023) by the same authors. It will appeal to a large audience, including specialists and newcomers to the field.




Error Estimation for Pattern Recognition


Book Description

This book is the first of its kind to discuss error estimation with a model-based approach. From the basics of classifiers and error estimators to distributional and Bayesian theory, it covers important topics and essential issues pertaining to the scientific validity of pattern classification. Error Estimation for Pattern Recognition focuses on error estimation, which is a broad and poorly understood topic that reaches all research areas using pattern classification. It includes model-based approaches and discussions of newer error estimators such as bolstered and Bayesian estimators. This book was motivated by the application of pattern recognition to high-throughput data with limited replicates, which is a basic problem now appearing in many areas. The first two chapters cover basic issues in classification error estimation, such as definitions, test-set error estimation, and training-set error estimation. The remaining chapters in this book cover results on the performance and representation of training-set error estimators for various pattern classifiers. Additional features of the book include: • The latest results on the accuracy of error estimation • Performance analysis of re-substitution, cross-validation, and bootstrap error estimators using analytical and simulation approaches • Highly interactive computer-based exercises and end-of-chapter problems This is the first book exclusively about error estimation for pattern recognition. Ulisses M. Braga Neto is an Associate Professor in the Department of Electrical and Computer Engineering at Texas A&M University, USA. He received his PhD in Electrical and Computer Engineering from The Johns Hopkins University. Dr. Braga Neto received an NSF CAREER Award for his work on error estimation for pattern recognition with applications in genomic signal processing. He is an IEEE Senior Member. Edward R. Dougherty is a Distinguished Professor, Robert F. Kennedy ’26 Chair, and Scientific Director at the Center for Bioinformatics and Genomic Systems Engineering at Texas A&M University, USA. He is a fellow of both the IEEE and SPIE, and he has received the SPIE Presidents Award. Dr. Dougherty has authored several books including Epistemology of the Cell: A Systems Perspective on Biological Knowledge and Random Processes for Image and Signal Processing (Wiley-IEEE Press).