Statistics for imaging, optics, and photonics:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Hoboken, N.J.
Wiley
2012
|
| Series: | Wiley series in probability and statistics
|
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Item Description: | Includes bibliographical references and index |
| Physical Description: | XIV, 379 S. graph. Darst. |
| ISBN: | 9780470509456 |
Staff View
MARC
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| 300 | |a XIV, 379 S. |b graph. Darst. | ||
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| 490 | 0 | |a Wiley series in probability and statistics | |
| 500 | |a Includes bibliographical references and index | ||
| 650 | 4 | |a Optics |x Statistical methods | |
| 650 | 4 | |a Image processing |x Statistical methods | |
| 650 | 4 | |a Photonics |x Statistical methods | |
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Record in the Search Index
| _version_ | 1804148677353144320 |
|---|---|
| adam_text | Titel: Statistics for imaging, optics, and photonics
Autor: Bajorski, Peter
Jahr: 2012
Contents
Preface xiii
1 Introduction 1
1.1 Who Should Read This Book, 6
1.2 How This Book is Organized, 6
1.3 How to Read This Book and Learn from It, 7
1.4 Note for Instructors, 8
1.5 Book Web Site, 9
2 Fundamentals of Statistics 11
2.1 Statistical Thinking, 11
2.2 Data Format, 13
2.3 Descriptive Statistics, 14
2.3.1 Measures of Location, 14
2.3.2 Measures of Variability, 16
2.4 Data Visualization, 17
2.4.1 Dot Plots, 17
2.4.2 Histograms, 19
2.4.3 Box Plots, 23
2.4.4 Scatter Plots, 24
2.5 Probability and Probability Distributions, 26
2.5.1 Probability and Its Properties, 26
2.5.2 Probability Distributions, 30
2.5.3 Expected Value and Moments, 33
2.5.4 Joint Distributions and Independence, 34
2.5.5 Covariance and Correlation, 38
2.6 Rules of Two and Three Sigma, 40
2.7 Sampling Distributions and the Laws of Large Numbers, 41
2.8 Skewness and Kurtosis, 44
3 Statistical Inference 51
3.1 Introduction, 51
3.2 Point Estimation of Parameters, 53
3.2.1 Definition and Properties of Estimators, 53
3.2.2 The Method of the Moments and Plug-In Principle, 56
3.2.3 The Maximum Likelihood Estimation, 57
3.3 Interval Estimation, 60
3.4 Hypothesis Testing, 63
3.5 Samples From Two Populations, 71
3.6 Probability Plots and Testing for Population
Distributions, 73
3.6.1 Probability Plots, 74
3.6.2 Kolmogorov-Smirnov Statistic, 75
3.6.3 Chi-Squared Test, 76
3.6.4 Ryan-Joiner Test for Normality, 76
3.7 Outlier Detection, 77
3.8 Monte Carlo Simulations, 79
3.9 Bootstrap, 79
4 Statistical Models 85
4.1 Introduction, 85
4.2 Regression Models, 85
4.2.1 Simple Linear Regression Model, 86
4.2.2 Residual Analysis, 94
4.2.3 Multiple Linear Regression and Matrix Notation, 96
4.2.4 Geometric Interpretation in an n-Dimensional Space, 99
4.2.5 Statistical Inference in Multiple Linear Regression, 100
4.2.6 Prediction of the Response and Estimation of the Mean
Response, 104
4.2.7 More on Checking the Model Assumptions, 107
4.2.8 Other Topics in Regression, 110
4.3 Experimental Design and Analysis, 111
4.3.1 Analysis of Designs with Qualitative Factors, 116
4.3.2 Other Topics in Experimental Design, 124
Supplement 4A. Vector and Matrix Algebra, 125
Vectors, 125
Matrices, 127
Eigenvalues and Eigenvectors of Matrices, 130
Spectral Decomposition of Matrices, 130
Positive Definite Matrices, 131
A Square Root Matrix, 131
Supplement 4B. Random Vectors and Matrices, 132
Sphering, 134
5 Fundamentals of Multivariate Statistics 137
5.1 Introduction, 137
5.2 The Multivariate Random Sample, 139
5.3 Multivariate Data Visualization, 143
5.4 The Geometry of the Sample, 148
5.4.1 The Geometric Interpretation of the Sample Mean, 148
5.4.2 The Geometric Interpretation of the Sample Standard
Deviation, 149
5.4.3 The Geometric Interpretation of the Sample Correlation
Coefficient, 150
5.5 The Generalized Variance, 151
5.6 Distances in the ^-Dimensional Space, 159
5.7 The Multivariate Normal (Gaussian) Distribution, 163
5.7.1 The Definition and Properties of the Multivariate
Normal Distribution, 163
5.7.2 Properties of the Mahalanobis Distance, 166
6 Multivariate Statistical Inference 173
6.1 Introduction, 173
6.2 Inferences About a Mean Vector, 173
6.2.1 Testing the Multivariate Population Mean, 173
6.2.2 Interval Estimation for the Multivariate
Population Mean, 175
6.2.3 f2 Confidence Regions, 179
6.3 Comparing Mean Vectors from Two Populations, 183
6.3.1 Equal Covariance Matrices, 184
6.3.2 Unequal Covariance Matrices and Large Samples, 185
6.3.3 Unequal Covariance Matrices and Samples Sizes
Not So Large, 186
6.4 Inferences About a Variance-Covariance Matrix, 187
6.5 How to Check Multivariate Normality, 188
Principal Component Analysis 193
7.1 Introduction, 193
7.2 Definition and Properties of Principal Components, 195
7.2.1 Definition of Principal Components, 195
7.2.2 Finding Principal Components, 196
7.2.3 Interpretation of Principal Component Loadings, 200
7.2.4 Scaling of Variables, 207
7.3 Stopping Rules for Principal Component Analysis, 209
7.3.1 Fair-Share Stopping Rules, 210
7.3.2 Large-Gap Stopping Rules, 213
7.4 Principal Component Scores, 217
7.5 Residual Analysis, 220
7.6 Statistical Inference in Principal Component Analysis, 227
7.6.1 Independent and Identically Distributed
Observations, 227
7.6.2 Imaging Related Sampling Schemes, 228
7.7 Further Reading, 238
Canonical Correlation Analysis 241
8.1 Introduction, 241
8.2 Mathematical Formulation, 242
8.3 Practical Application, 245
8.4 Calculating Variability Explained by Canonical
Variables, 246
8.5 Canonical Correlation Regression, 251
8.6 Further Reading, 256
Supplement 8A. Cross-Validation, 256
Discrimination and Classification - Supervised Learning 261
9.1 Introduction, 261
9.2 Classification for Two Populations, 264
9.2.1 Classification Rules for Multivariate
Normal Distributions, 267
9.2.2 Cross-Validation of Classification Rules, 277
9.2.3 Fisher s Discriminant Function, 280
9.3 Classification for Several Populations, 284
9.3.1 Gaussian Rules, 284
9.3.2 Fisher s Method, 286
9.4 Spatial Smoothing for Classification, 291
9.5 Further Reading, 293
10 Clustering - Unsupervised Learning 297
10.1 Introduction, 297
10.2 Similarity and Dissimilarity Measures, 298
10.2.1 Similarity and Dissimilarity Measures
for Observations, 298
10.2.2 Similarity and Dissimilarity Measures for
Variables and Other Objects, 304
10.3 Hierarchical Clustering Methods, 304
10.3.1 Single Linkage Algorithm, 305
10.3.2 Complete Linkage Algorithm, 312
10.3.3 Average Linkage Algorithm, 315
10.3.4 Ward Method, 319
10.4 Nonhierarchical Clustering Methods, 320
10.4.1 K-Means Method, 320
10.5 Clustering Variables, 323
10.6 Further Reading, 325
Appendix A Probability Distributions 329
Appendix B Data Sets 349
Appendix C Miscellanea 355
References 365
Index 371
|
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| illustrated | Illustrated |
| indexdate | 2024-07-10T00:10:56Z |
| institution | BVB |
| isbn | 9780470509456 |
| language | English |
| lccn | 2011015224 |
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| spelling | Bajorski, Peter 1958- Verfasser (DE-588)1017823758 aut Statistics for imaging, optics, and photonics Peter Bajorski Hoboken, N.J. Wiley 2012 XIV, 379 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Wiley series in probability and statistics Includes bibliographical references and index Optics Statistical methods Image processing Statistical methods Photonics Statistical methods MATHEMATICS / Probability & Statistics / Multivariate Analysis bisacsh HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=024625192&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Bajorski, Peter 1958- Statistics for imaging, optics, and photonics Optics Statistical methods Image processing Statistical methods Photonics Statistical methods MATHEMATICS / Probability & Statistics / Multivariate Analysis bisacsh |
| title | Statistics for imaging, optics, and photonics |
| title_auth | Statistics for imaging, optics, and photonics |
| title_exact_search | Statistics for imaging, optics, and photonics |
| title_full | Statistics for imaging, optics, and photonics Peter Bajorski |
| title_fullStr | Statistics for imaging, optics, and photonics Peter Bajorski |
| title_full_unstemmed | Statistics for imaging, optics, and photonics Peter Bajorski |
| title_short | Statistics for imaging, optics, and photonics |
| title_sort | statistics for imaging optics and photonics |
| topic | Optics Statistical methods Image processing Statistical methods Photonics Statistical methods MATHEMATICS / Probability & Statistics / Multivariate Analysis bisacsh |
| topic_facet | Optics Statistical methods Image processing Statistical methods Photonics Statistical methods MATHEMATICS / Probability & Statistics / Multivariate Analysis |
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