Analysis of Experimental Data in Science and Technology / Andrzej Zieba.

Format:

Book

Author/Creator:

Zięba, Andrzej, author.

Language:

English

Subjects (All):

Artificial intelligence.

Computational complexity.

Computational intelligence.

Physical Description:

1 online resource (0 pages)

Edition:

First edition.

Place of Publication:

Newcastle upon Tyne, England : Cambridge Scholars Publishing, [2023]

Summary:

This textbook presents methods of data analysis and uncertainty estimation based on classical statistics whilst including the use of robust statistics, Monte Carlo modelling, informational criteria, and non-statistical methods. Related computer programs and their creative use are also discussed, without reference to specific packages. The book contains one hundred illustrations and numerous examples using real-world data, from a student lab to the latest scientific results. It will appeal to students, scientists, engineers, metrologists, and everyone interested in processing measurement results.

Contents:

Intro

Contents

Preface

Chapter 1

1.1. Physical and non-physical quantities

1.2. Coherent systems of units

1.3. International System of Units (SI) and its base units

1.4. Derived SI units

1.5. Decimal multiples and submultiples of units

1.6. Units of physical quantities outside the SI

1.7. Calculations on numbers with units

Chapter 2

2.1. Discrete nature of numbers from a measuring device

2.2. Significant and insignificant digits

2.3. Calculations on numbers with finite resolution

2.4. Pocket calculator

2.5. Computer

Chapter 3

3.1. Basic definitions

3.2. Traditional classification of errors

3.3. Outliers

3.4. Various theoretical approaches to error phenomena

3.5. Description of measurement accuracy adopted by the GUM

Chapter 4

4.1. Processing of data from repeated measurement

4.2. Accuracy of the statistical evaluation of uncertainty

4.3. Standard uncertainty reporting

4.4. Other instances of Type A uncertainty assessment

Chapter 5

5.1. Assumptions about the standard Type A method and their denials

5.2. Simultaneous occurrence of random and systematic error

5.3. Non-equivalent observations. The weighted mean

5.4. Interlaboratory comparisons

5.5. Serially correlated observations

5.6. Detection of outliers using the Grubbs test

5.7. Applying robust statistics to data with outliers

5.8. Interlaboratory comparisons: robust statistics

5.9. Repeated measurement in interval theory

Chapter 6

6.1. Digital and analogue meters

6.2. Converting the limiting uncertainty into the standard uncertainty

6.3. Use of information from previous measurements

6.4. Uncertainty of the average number of random events

6.5. Subjective assessment of uncertainty

Chapter 7

7.1. Mathematical model of measurement.

7.2. Uncertainty propagation for functions of one variable

7.3. General law of uncertainty propagation

7.4. Propagation of relative uncertainties

7.5. Correlated input variables

7.6. Final remarks

Chapter 8

8.1. Calculation and reporting of the expanded uncertainty

8.2. Comparing the measurement result with the exact value

8.3. Compatibility of the results of two measurements

8.4. Statistical coverage interval for repeated measurement

8.5. Stochastic properties of the combined uncertainty

8.6. Composition of the normal and rectangular distribution

8.7. Relation to statistical hypotheses testing

Chapter 9

9.1. Coordinate system

9.2. Experimental points

9.3. Curve interpreting experimental data

9.4. Histogram

9.5. Final remarks

Chapter 10

10.1. Graphical method

10.2. Least squares method

10.3. Uncertainty of fit parameters

10.4. A straight line through the origin of the coordinate system

10.5. Transformation of nonlinear functions to a linear relationship

10.6. Influence of gross errors, systematic errors, and outliers

Chapter 11

11.1. Maximum likelihood principle

11.2. Derivation of the least-squares method

11.3. Overview of variants of the least-squares method

11.4. Fit parameters as estimators

11.5. Stochastic properties of the merit function minimum

11.6. Errors in both coordinates

11.7. Fitting a constant function

Chapter 12

12.1. Matrix formalism of the LS method

12.2. Uncertainty of fit parameters

12.3. Correlation between slope and intercept values

12.4. Fixing one of the fit parameters

12.5. Use of centred data

12.6. Linear dependence as a calibration function

12.7. Finite uncertainties for both variables

12.8. Correlation coefficient between independent and dependent variable

Chapter 13.

13.1. General formalism of the LLS method

13.2. Fitting of a polynomial

13.3. Centred and normalized independent variable

13.4. Orthogonal polynomials

13.5. Calibration employing a polynomial function

13.6. Extrapolation beyond the range of data points

13.7. Tangent to a function determined by experimental points

13.8. Piecewise functions and splines

13.9. Generalization to a larger number of independent and dependent variables

Chapter 14

14.1. Merit function: global characteristics and those in the vicinity of its minimum

14.2. Starting values of fit parameters

14.3. Search for the minimum of a merit function

14.4. Uncertainties of the fit parameters

14.5. Linear parameters in the NLS method

Chapter 15

15.1. Graph of fit residuals

15.2. More on the formalism of the LS method. Studentized residuals

15.3. Chi-squared test

15.4. Signs of residuals

15.5. Using the merit function: F-test

15.6. Testing the relevance of fit parameters

15.7. Akaike information criterion

Chapter 16

16.1. Occurrence of systematic errors

16.2. Testing uniformity of error magnitude

16.3. Serially correlated residuals

16.4. Investigation of the probability distribution of residuals

16.5. Normality tests

Chapter 17

17.1. Graphical method revisited

17.2. Fitting a straight line in interval theory

17.3. Serially correlated errors

17.4. Robust fitting methods using M-estimators

17.5. Methods employing other modifications of the merit function

Chapter 18

18.1. Random numbers and their use to model measurement errors

18.2. Propagation of probability distributions

18.3. Coverage interval obtained using the MC method

18.4. Standard uncertainty in the propagation of distributions method

18.5. Correlations and autocorrelation.

18.6. Determining uncertainties of parameters of the fitted function

18.7. Resampling methods

18.8. Final remarks

Appendix A

A1. Discrete and continuous random variable

A2. Parameters of location and scale

A3. Sums and linear combinations of random variables

A4. Central limit theorem

Appendix B

B1. Elementary example and terminology

B2. Estimator as a random variable

B3. Properties of estimators

B4. Arithmetic mean

B5. Three estimators of variance

B6. Estimator of standard deviation

B7. Coverage interval

B8. More on the efficiency of estimators

B9. Estimation theory as a branch of mathematical statistics

Appendix C

Appendix D

D1. Basic concepts

D2. Elementary example: testing the reliability of a die

D3. Practical implementation of tests. The p-value

D4. Final remarks

Appendix E

E1. Definition and description of statistically dependent variables

E2. Covariance and correlation coefficient

E3. Sum and linear combination of correlated variables

E4. Bivariate normal distribution

E5. Serially correlated random sample. Autocorrelation function

E6. Stationary time series

E7. Estimators of location and scale for known ACF

E8. Autocorrelation function estimated from the sample

E9. Estimators employing the ACF derived from a sample

Appendix F

F1. The genesis of robust statistics

F2. Probability distributions with heavy tails

F3. Examples of non-robust and robust estimators of location

F4. Estimators of scale

F5. Quantities characterizing robust estimators

F6. M-estimators of location

F7. M-estimators calculated using the iteratively reweighted least squares method

F8. Final remarks

Appendix G

G1. Genesis and creation of the GUM Guide

G2. Supplements to the GUM

G3. Derivative documents. Reception and relevance of the GUM.

References

Index.

Notes:

Description based on print version record.

Includes bibliographical references and index.

Other Format:

Print version: Zięba, Andrzej Analysis of Experimental Data in Science and Technology

ISBN:

1-5275-0449-2