This book is about methodological aspects of uncertainty propagation in data processing. Uncertainty propagation is an important problem: while computer algorithms efficiently process data related to many aspects of their lives, most of these algorithms implicitly assume that the numbers they process are exact. In reality, these numbers come from measurements, and measurements are never 100% exact. Because of this, it makes no sense to translate 61 kg into pounds and get the result—as computers do—with 13 digit accuracy. In many cases—e.g., in celestial mechanics—the state of a system can be described by a few numbers: the values of the corresponding physical quantities. In such cases, for each of these quantities, we know (at least) the upper bound on the measurement error. This bound is either provided by the manufacturer of the measuring instrument—or is estimated by the user who calibrates this instrument. However, in many other cases, the description of the system is more complex than a few numbers: we need a function to describe a physical field (e.g., electromagnetic field); we need a vector in Hilbert space to describe a quantum state; we need a pseudo-Riemannian space to describe the physical space-time, etc. To describe and process uncertainty in all such cases, this book proposes a general methodology—a methodology that includes intervals as a particular case. The book is recommended to students and researchers interested in challenging aspects of uncertainty analysis and to practitioners who need to handle uncertainty in such unusual situations.

Fast After 50 is for every endurance athlete who wants to stay fast for years to come. For runners, cyclists, triathletes, swimmers, and cross-country skiers, getting older doesn’t have to mean getting slower. Drawing from the most current research on aging and sports performance, Joe Friel--America’s leading endurance sports coach--shows how athletes can race strong and stay healthy well past age 50. In his groundbreaking book Fast After 50, Friel offers a smart approach for athletes to ward off the effects of age. Friel shows athletes how to extend their racing careers for decades--and race to win. Fast After 50 presents guidelines for high-intensity workouts, focused strength training, recovery, crosstraining, and nutrition for high performance: How the body’s response to training changes with age, how to adapt your training plan, and how to avoid overtraining How to shed body fat and regain muscle density How to create a progressive plan for training, rest, recovery, and competition Workout guidelines, field tests, and intensity measurement In Fast After 50, Joe Friel shows athletes that age is just a number--and race results are the only numbers that count. With contributions from: Mark Allen, Gale Bernhardt, Amby Burfoot, Dr. Larry Creswell, John Howard, Dr. Tim Noakes, Ned Overend, Dr. John Post, Dr. Andrew Pruitt, and Lisa Rainsberger.

Presents training principles for the multisport mountain athlete who regularly participates in a mix of distance running, ski mountaineering, and other endurance sports that require optimum fitness and customized strength

Presents a detailed exposition of statistical intervals and emphasizes applications in industry. The discussion differentiates at an elementary level among different kinds of statistical intervals and gives instruction with numerous examples and simple math on how to construct such intervals from sample data. This includes confidence intervals to contain a population percentile, confidence intervals on probability of meeting specified threshold value, and prediction intervals to include observation in a future sample. Also has an appendix containing computer subroutines for nonparametric statistical intervals.

Iterations of continuous maps of an interval to itself serve as the simplest examples of models for dynamical systems. These models present an interesting mathematical structure going far beyond the simple equilibrium solutions one might expect. If, in addition, the dynamical system depends on an experimentally controllable parameter, there is a corresponding mathematical structure revealing a great deal about interrelations between the behavior for different parameter values. This work explains some of the early results of this theory to mathematicians and theoretical physicists, with the additional hope of stimulating experimentalists to look for more of these general phenomena of beautiful regularity, which oftentimes seem to appear near the much less understood chaotic systems. Although continuous maps of an interval to itself seem to have been first introduced to model biological systems, they can be found as models in most natural sciences as well as economics. Iterated Maps on the Interval as Dynamical Systems is a classic reference used widely by researchers and graduate students in mathematics and physics, opening up some new perspectives on the study of dynamical systems .

Describes statistical intervals to quantify sampling uncertainty,focusing on key application needs and recently developed methodology in an easy-to-apply format Statistical intervals provide invaluable tools for quantifying sampling uncertainty. The widely hailed first edition, published in 1991, described the use and construction of the most important statistical intervals. Particular emphasis was given to intervals—such as prediction intervals, tolerance intervals and confidence intervals on distribution quantiles—frequently needed in practice, but often neglected in introductory courses. Vastly improved computer capabilities over the past 25 years have resulted in an explosion of the tools readily available to analysts. This second edition—more than double the size of the first—adds these new methods in an easy-to-apply format. In addition to extensive updating of the original chapters, the second edition includes new chapters on: Likelihood-based statistical intervals Nonparametric bootstrap intervals Parametric bootstrap and other simulation-based intervals An introduction to Bayesian intervals Bayesian intervals for the popular binomial, Poisson and normal distributions Statistical intervals for Bayesian hierarchical models Advanced case studies, further illustrating the use of the newly described methods New technical appendices provide justification of the methods and pathways to extensions and further applications. A webpage directs readers to current readily accessible computer software and other useful information. Statistical Intervals: A Guide for Practitioners and Researchers, Second Edition is an up-to-date working guide and reference for all who analyze data, allowing them to quantify the uncertainty in their results using statistical intervals.

An update on the author's previous books, this introduction to interval analysis provides an introduction to INTLAB, a high-quality, comprehensive MATLAB toolbox for interval computations, making this the first interval analysis book that does with INTLAB what general numerical analysis texts do with MATLAB.

Shave minutes off your time using the latest in science-based training for serious runners. Advanced Marathoning has all the information you need to train smarter, remain injury free, and arrive on the start line ready to run the marathon of your life. Including marathon-pace runs and tempo runs, Advanced Marathoning provides only the most effective methods of training. You'll learn how to complement your running workouts with strength, core, flexibility, and form training; implement cutting-edge nutrition and hydration strategies and recovery techniques; and taper properly to reach peak performance. With easy-to-understand day-by-day training schedules for 18- and 12-week preparation for weekly distances of 55, 55 to 70, 70 to 85, and 85-plus miles, Advanced Marathoning is simply the most comprehensive and efficient approach to marathoning. If you're ready to achieve your personal best, this book is for you.

This highly popular introduction to confidence intervals has been thoroughly updated and expanded. It includes methods for using confidence intervals, with illustrative worked examples and extensive guidelines and checklists to help the novice.