Drosg Dealing with Uncertainties

A Guide to Error Analysis
2007
ISBN: 978-3-540-29608-9
Verlag: Springer Berlin Heidelberg
Format: PDF
Kopierschutz: 1 - PDF Watermark

E-Book, Englisch, 190 Seiten

Dealing with Uncertainties proposes and explains a new approach for the analysis of uncertainties. Firstly, it is shown that uncertainties are the consequence of modern science rather than of measurements. Secondly, it stresses the importance of the deductive approach to uncertainties. This perspective has the potential of dealing with the uncertainty of a single data point and of data of a set having differing weights. Both cases cannot be dealt with the inductive approach, which is usually taken. This innovative monograph also fully covers both uncorrelated and correlated uncertainties. The weakness of using statistical weights in regression analysis is discussed. Abundant examples are given for correlation in and between data sets and for the feedback of uncertainties on experiment design.

Autoren/Hrsg.

Drosg, Manfred

Inhaltsverzeichnis

1;Preface;6
2;Foreword by the Translator;8
3;Prolog. Seven Myths in Error Analysis;9
4;Contents;11
5;1 Introduction;13
5.1;1.1 The Exactness of Science;14
5.2;1.2 Data Without Uncertainty;16
6;2 Basics on Data;18
6.1;2.1 What Is a Measurement?;19
6.2;2.2 Analog vs. Digital;22
6.3;2.3 Dealing With Data (Numerals);23
7;3 Basics on Uncertainties (Errors);26
7.1;3.1 Typical Sources of Internal Uncertainties;27
7.2;3.2 Definitions;28
7.3;3.3 Uncertainty of Data Depending on One Variable;37
7.4;3.4 Multiple Uncertainty Components (Quadratic Sum);38
8;4 Radioactive Decay, a Model for Random Events;43
8.1;4.1 Time Interval Distribution of Radioactive Events;43
8.2;4.2 Inductive Approach to Uncertainty (Example);49
9;5 Frequency and Probability Distributions;60
9.1;5.1 Frequency Distribution (Spectrum);60
9.2;5.2 Probability Distributions;67
9.3;5.3 Statistical Confidence;74
9.4;5.4 Dealing With Probabilities;75
10;6 Deductive Approach to Uncertainty;79
10.1;6.1 Theoretical Situation;79
10.2;6.2 Practical Situation;79
10.3;6.3 Regression Analysis (Least-Squares Method);89
10.4;6.4 Data Consistency Within Data Sets;95
11;7 Correlation;98
11.1;7.1 Introduction;98
11.2;7.2 Correlated (Systematic) Internal Uncertainties;100
11.3;7.3 Differentiation From "Systematic Errors”;111
11.4;7.4 Correlation in Cases of Linear Regression;115
11.5;7.5 Data Consistency Among Data Sets;120
11.6;7.6 Target Shooting as a Model for Uncertainties;125
12;8 Dealing With Internal Uncertainties;127
12.1;8.1 Calculations With Both Types of Uncertainties;130
12.2;8.2 Total Uncertainty;138
12.3;8.3 Using Internal Uncertainties for Diagnosis;141
13;9 Presentation and Estimation of Uncertainties;146
13.1;9.1 Graphic Presentation, Also of Uncertainties;146
13.2;9.2 Correct Presentation of Uncertainties;150
13.3;9.3 Finding the Size of Internal Uncertainties;151
13.4;9.4 Estimating the Size of (Internal) Uncertainties;153
14;10 Feedback of Uncertainties on Experiment Design;157
14.1;10.1 Optimizing Experiments;157
14.2;10.2 Optimizing Background Measurements;159
14.3;10.3 Optimizing With Respect to Dead Time;162
14.4;10.4 Optimizing in View of the Mathematical Presentation;164
14.5;10.5 Achieving the Smallest Overall Uncertainty;166
15;Solutions;174
16;Index;182