Environmental Data Analysis with MatLab

Table of contents

1. Cover image
2. Table of Contents
3. Front matter
4. Copyright
5. Dedication
6. Preface
7. Advice on scripting for beginners
8. 1. Data analysis with MatLab
9. 1.1. Why MatLab?
10. 1.2. Getting started with MatLab
11. 1.3. Getting organized
12. 1.4. Navigating folders
13. 1.5. Simple arithmetic and algebra
14. 1.6. Vectors and matrices
15. 1.7. Multiplication of vectors of matrices
16. 1.8. Element access
17. 1.9. To loop or not to loop
18. 1.10. The matrix inverse
19. 1.11. Loading data from a file
20. 1.12. Plotting data
21. 1.13. Saving data to a file
22. 1.14. Some advice on writing scripts
23. 2. A first look at data
24. 2.1. Look at your data!
25. 2.2. More on MatLab graphics
26. 2.3. Rate information
27. 2.4. Scatter plots and their limitations
28. 3. Probability and what it has to do with data analysis
29. 3.1. Random variables
30. 3.2. Mean, median, and mode
31. 3.3. Variance
32. 3.4. Two important probability density functions
33. 3.5. Functions of a random variable
34. 3.6. Joint probabilities
35. 3.7. Bayesian inference
36. 3.8. Joint probability density functions
37. 3.9. Covariance
38. 3.10. Multivariate distributions
39. 3.11. The multivariate Normal distributions
40. 3.12. Linear functions of multivariate data
41. 4. The power of linear models
42. 4.1. Quantitative models, data, and model parameters
43. 4.2. The simplest of quantitative models
44. 4.3. Curve fitting
45. 4.4. Mixtures
46. 4.5. Weighted averages
47. 4.6. Examining error
48. 4.7. Least squares
49. 4.8. Examples
50. 4.9. Covariance and the behavior of error
51. 5. Quantifying preconceptions
52. 5.1. When least square fails
53. 5.2. Prior information
54. 5.3. Bayesian inference
55. 5.4. The product of Normal probability density distributions
56. 5.5. Generalized least squares
57. 5.6. The role of the covariance of the data
58. 5.7. Smoothness as prior information
59. 5.8. Sparse matrices
60. 5.9. Reorganizing grids of model parameters
61. 6. Detecting periodicities
62. 6.1. Describing sinusoidal oscillations
63. 6.2. Models composed only of sinusoidal functions
64. 6.3. Going complex
65. 6.4. Lessons learned from the integral transform
66. 6.5. Normal curve
67. 6.6. Spikes
68. 6.7. Area under a function
69. 6.8. Time-delayed function
70. 6.9. Derivative of a function
71. 6.10. Integral of a function
72. 6.11. Convolution
73. 6.12. Nontransient signals
74. 7. The past influences the present
75. 7.1. Behavior sensitive to past conditions
76. 7.2. Filtering as convolution
77. 7.3. Solving problems with filters
78. 7.4. Predicting the future
79. 7.5. A parallel between filters and polynomials
80. 7.6. Filter cascades and inverse filters
81. 7.7. Making use of what you know
82. 8. Patterns suggested by data
83. 8.1. Samples as mixtures
84. 8.2. Determining the minimum number of factors
85. 8.3. Application to the Atlantic Rocks dataset
86. 8.4. Spiky factors
87. 8.5. Time-Variable functions
88. 9. Detecting correlations among data
89. 9.1. Correlation is covariance
90. 9.2. Computing autocorrelation by hand
91. 9.3. Relationship to convolution and power spectral density
92. 9.4. Cross-correlation
93. 9.5. Using the cross-correlation to align time series
94. 9.6. Least squares estimation of filters
95. 9.7. The effect of smoothing on time series
96. 9.8. Band-pass filters
97. 9.9. Frequency-dependent coherence
98. 9.10. Windowing before computing Fourier transforms
99. 9.11. Optimal window functions
100. 10. Filling in missing data
101. 10.1. Interpolation requires prior information
102. 10.2. Linear interpolation
103. 10.3. Cubic interpolation
104. 10.4. Kriging
105. 10.5. Interpolation in two-dimensions
106. 10.6. Fourier transforms in two dimensions
107. 11. Are my results significant?
108. 11.1. The difference is due to random variation!
109. 11.2. The distribution of the total error
110. 11.3. Four important probability density functions
111. 11.4. A hypothesis testing scenario
112. 11.5. Testing improvement in fit
113. 11.6. Testing the significance of a spectral peak
114. 11.7. Bootstrap confidence intervals
115. 12. Notes
116. Note 1.1. On the persistence of MatLab variables
117. Note 2.1. On time
118. Note 2.2. On reading complicated text files
119. Note 3.1. On the rule for error propagation
120. Note 3.2. On the eda_draw() function
121. Note 4.1. On complex least squares
122. Note 5.1. On the derivation of generalized least squares
123. Note 5.2. On MatLab functions
124. Note 5.3. On reorganizing matrices
125. Note 6.1. On the MatLabatan2() function
126. Note 6.2. On the orthonormality of the discrete Fourier data kernel
127. Note 8.1. On singular value decomposition
128. Note 9.1. On coherence
129. Note 9.2. On Lagrange multipliers
130. Index