Menke Environmental Data Analysis with MatLab

1. Auflage 2009
ISBN: 978-0-12-391887-1
Verlag: Elsevier Science & Techn.
Format: EPUB
Kopierschutz: 6 - ePub Watermark

E-Book, Englisch, 288 Seiten

Environmental Data Analysis with MatLab is a reference work designed to teach students and researchers the basics of data analysis in the environmental sciences using MatLab, and more specifically how to analyze data sets in carefully chosen, realistic scenarios. Although written in a self-contained way, the text is supplemented with data sets and MatLab scripts that can be used as a data analysis tutorial, available at the author's website: http://www.ldeo.columbia.edu/users/menke/edawm/index.htm. This book is organized into 12 chapters. After introducing the reader to the basics of data analysis with MatLab, the discussion turns to the power of linear models; quantifying preconceptions; detecting periodicities; patterns suggested by data; detecting correlations among the data; filling in missing data; and determining whether your results are significant. Homework problems help users follow up upon case studies. This text will appeal to environmental scientists, specialists, researchers, analysts, and undergraduate and graduate students in Environmental Engineering, Environmental Biology and Earth Science courses, who are working to analyze data and communicate results. - Well written and outlines a clear learning path for researchers and students - Uses real world environmental examples and case studies - MatLab software for application in a readily-available software environment - Homework problems help user follow up upon case studies with homework that expands them

William Menke is a Professor of Earth and Environmental Sciences at Columbia University. His research focuses on the development of data analysis algorithms for time series analysis and imaging in the earth and environmental sciences and the application of these methods to volcanoes, earthquakes, and other natural hazards. He has thirty years of experience teaching data analysis methods to both undergraduates and graduate students. Relevant courses that he has taught include, at the undergraduate level, Environmental Data Analysis and The Earth System, and at the graduate level, Geophysical Inverse Theory, Quantitative Methods of Data Analysis, Geophysical Theory and Practical Seismology.

Autoren/Hrsg.

Menke, William

Menke, Joshua

Inhaltsverzeichnis

1;Front Cover;1
2;Environmental Data Analysis with MatLab;4
3;Copyright;5
4;Dedication;6
5;Preface;8
6;Advice on scripting for beginners;14
7;Contents;16
8;Chapter 1: Data analysis with MatLab;20
8.1;1.1. Why MatLab?;20
8.2;1.2. Getting started with MatLab;22
8.3;1.3. Getting organized;22
8.4;1.4. Navigating folders;23
8.5;1.5. Simple arithmetic and algebra;24
8.6;1.6. Vectors and matrices;26
8.7;1.7. Multiplication of vectors of matrices;26
8.8;1.8. Element access;27
8.9;1.9. To loop or not to loop;28
8.10;1.10. The matrix inverse;30
8.11;1.11. Loading data from a file;30
8.12;1.12. Plotting data;31
8.13;1.13. Saving data to a file;32
8.14;1.14. Some advice on writing scripts;32
8.15;Problems;34
9;Chapter 2: A first look at data;36
9.1;2.1. Look at your data!;36
9.2;2.2. More on MatLab graphics;43
9.3;2.3. Rate information;47
9.4;2.4. Scatter plots and their limitations;49
9.5;Problems;52
10;Chapter 3: Probability and what it has to do with data analysis;54
10.1;3.1. Random variables;54
10.2;3.2. Mean, median, and mode;56
10.3;3.3. Variance;60
10.4;3.4. Two important probability density functions;61
10.5;3.5. Functions of a random variable;63
10.6;3.6. Joint probabilities;65
10.7;3.7. Bayesian inference;67
10.8;3.8. Joint probability density functions;68
10.9;3.9. Covariance;71
10.10;3.10. Multivariate distributions;73
10.11;3.11. The multivariate Normal distributions;73
10.12;3.12. Linear functions of multivariate data;76
10.13;Problems;79
11;Chapter 4: The power of linear models;80
11.1;4.1. Quantitative models, data, and model parameters;80
11.2;4.2. The simplest of quantitative models;82
11.3;4.3. Curve fitting;83
11.4;4.4. Mixtures;86
11.5;4.5. Weighted averages;87
11.6;4.6. Examining error;90
11.7;4.7. Least squares;93
11.8;4.8. Examples;95
11.9;4.9. Covariance and the behavior of error;98
11.10;Problems;100
12;Chapter 5: Quantifying preconceptions;102
12.1;5.1. When least square fails;102
12.2;5.2. Prior information;103
12.3;5.3. Bayesian inference;105
12.4;5.4. The product of Normal probability density distributions;107
12.5;5.5. Generalized least squares;109
12.6;5.6. The role of the covariance of the data;111
12.7;5.7. Smoothness as prior information;112
12.8;5.8. Sparse matrices;114
12.9;5.9. Reorganizing grids of model parameters;117
12.10;Problems;120
13;Chapter 6: Detecting periodicities;122
13.1;6.1. Describing sinusoidal oscillations;122
13.2;6.2. Models composed only of sinusoidal functions;124
13.3;6.3. Going complex;131
13.4;6.4. Lessons learned from the integral transform;133
13.5;6.5. Normal curve;134
13.6;6.6. Spikes;135
13.7;6.7. Area under a function;137
13.8;6.8. Time-delayed function;137
13.9;6.9. Derivative of a function;139
13.10;6.10. Integral of a function;139
13.11;6.11. Convolution;140
13.12;6.12. Nontransient signals;141
13.13;Problems;143
14;Chapter 7: The past influences the present;146
14.1;7.1. Behavior sensitive to past conditions;146
14.2;7.2. Filtering as convolution;150
14.3;7.3. Solving problems with filters;151
14.4;7.4. Predicting the future;158
14.5;7.5. A parallel between filters and polynomials;159
14.6;7.6. Filter cascades and inverse filters;161
14.7;7.7. Making use of what you know;164
14.8;Problems;166
15;Chapter 8: Patterns suggested by data;168
15.1;8.1. Samples as mixtures;168
15.2;8.2. Determining the minimum number of factors;170
15.3;8.3. Application to the Atlantic Rocks dataset;174
15.4;8.4. Spiky factors;175
15.5;8.5. Time-Variable functions;179
15.6;Problems;182
16;Chapter 9: Detecting correlations among data;186
16.1;9.1. Correlation is covariance;186
16.2;9.2. Computing autocorrelation by hand;192
16.3;9.3. Relationship to convolution and power spectral density;192
16.4;9.4. Cross-correlation;193
16.5;9.5. Using the cross-correlation to align time series;195
16.6;9.6. Least squares estimation of filters;197
16.7;9.7. The effect of smoothing on time series;199
16.8;9.8. Band-pass filters;203
16.9;9.9. Frequency-dependent coherence;207
16.10;9.10. Windowing before computing Fourier transforms;214
16.11;9.11. Optimal window functions;215
16.12;Problems;220
17;Chapter 10: Filling in missing data;222
17.1;10.1. Interpolation requires prior information;222
17.2;10.2. Linear interpolation;224
17.3;10.3. Cubic interpolation;225
17.4;10.4. Kriging;227
17.5;10.5. Interpolation in two-dimensions;229
17.6;10.6. Fourier transforms in two dimensions;232
17.7;Problems;234
18;Chapter 11: Are my results significant?;236
18.1;11.1. The difference is due to random variation!;236
18.2;11.2. The distribution of the total error;237
18.3;11.3. Four important probability density functions;239
18.4;11.4. A hypothesis testing scenario;241
18.5;11.5. Testing improvement in fit;247
18.6;11.6. Testing the significance of a spectral peak;248
18.7;11.7. Bootstrap confidence intervals;253
18.8;Problems;257
19;Chapter 12: Notes;258
19.1;Note 1.1. On the persistence of MatLab variables;258
19.2;Note 2.1. On time;259
19.3;Note 2.2. On reading complicated text files;260
19.4;Note 3.1. On the rule for error propagation;261
19.5;Note 3.2. On the eda_draw() function;261
19.6;Note 4.1. On complex least squares;262
19.7;Note 5.1. On the derivation of generalized least squares;264
19.8;Note 5.2. On MatLab functions;264
19.9;Note 5.3. On reorganizing matrices;265
19.10;Note 6.1. On the MatLab atan2() function;265
19.11;Note 6.2. On the orthonormality of the discrete Fourier data kernel;265
19.12;Note 8.1. On singular value decomposition;266
19.13;Note 9.1. On coherence;267
19.14;Note 9.2. On Lagrange multipliers;268
20;Index;270