# Measurement Uncertainty and Probability

## Book Description

A measurement result is incomplete without a statement of its 'uncertainty' or 'margin of error'. But what does this statement actually tell us? By examining the practical meaning of probability, this book discusses what is meant by a '95 percent interval of measurement uncertainty', and how such an interval can be calculated. The book argues that the concept of an unknown 'target value' is essential if probability is to be used as a tool for evaluating measurement uncertainty. It uses statistical concepts, such as a conditional confidence interval, to present 'extended' classical methods for evaluating measurement uncertainty. The use of the Monte Carlo principle for the simulation of experiments is described. Useful for researchers and graduate students, the book also discusses other philosophies relating to the evaluation of measurement uncertainty. It employs clear notation and language to avoid the confusion that exists in this controversial field of science.

### Table of Contents

Part I Principles

Chapter 1 Foundational ideas in measurement

Chapter 2 Components of error or uncertainty

Chapter 3 Foundational ideas in probability and statistics

Chapter 4 The randomization of systematic errors

Chapter 5 Beyond the ordinary conﬁdence interval

Part II Evaluation of uncertainty

Chapter 6 Final preparation

Chapter 7 Evaluation using the linear approximation

Chapter 8 Evaluation without the linear approximation

Chapter 9 Uncertainty information ﬁt for purpose

Part III Related topics

Chapter 10 Measurement of vectors and functions

Chapter 11 Why take part in a measurement comparison?

Chapter 12 Other philosophies

Chapter 13 An assessment of objective Bayesian statistics

Chapter 14 Guide to the Expression of Uncertainty in Measurement

Chapter 15 Measurement near a limit – an insoluble problem?

Appendix A The weak law of large numbers

Appendix B The Sleeping Beauty paradox

Appendix C The sum of normal and uniform variates

Appendix D Analysis with one Type A and one Type B error

Appendix E Conservatism of treatment of Type A errors

## Book Details

- Title: Measurement Uncertainty and Probability
- Author: Robin Willink
- Length: 291 pages
- Edition: 1
- Language: English
- Publisher: Cambridge University Press
- Publication Date: 2013-03-29
- ISBN-10: 1107021936
- ISBN-13: 9781107021938

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