Environmental Data Analysis with Mat: Lab

Front Cover......Page 1
Environmental Data Analysis with MatLab......Page 4
Copyright......Page 5
Dedication......Page 6
Preface......Page 8
Advice on scripting for beginners......Page 14
Contents......Page 16
1.1. Why MatLab?......Page 20
1.3. Getting organized......Page 22
1.4. Navigating folders......Page 23
1.5. Simple arithmetic and algebra......Page 24
1.7. Multiplication of vectors of matrices......Page 26
1.8. Element access......Page 27
1.9. To loop or not to loop......Page 28
1.11. Loading data from a file......Page 30
1.12. Plotting data......Page 31
1.14. Some advice on writing scripts......Page 32
Problems......Page 34
2.1. Look at your data!......Page 36
2.2. More on MatLab graphics......Page 43
2.3. Rate information......Page 47
2.4. Scatter plots and their limitations......Page 49
Problems......Page 52
3.1. Random variables......Page 54
3.2. Mean, median, and mode......Page 56
3.3. Variance......Page 60
3.4. Two important probability density functions......Page 61
3.5. Functions of a random variable......Page 63
3.6. Joint probabilities......Page 65
3.7. Bayesian inference......Page 67
3.8. Joint probability density functions......Page 68
3.9. Covariance......Page 71
3.11. The multivariate Normal distributions......Page 73
3.12. Linear functions of multivariate data......Page 76
Problems......Page 79
4.1. Quantitative models, data, and model parameters......Page 80
4.2. The simplest of quantitative models......Page 82
4.3. Curve fitting......Page 83
4.4. Mixtures......Page 86
4.5. Weighted averages......Page 87
4.6. Examining error......Page 90
4.7. Least squares......Page 93
4.8. Examples......Page 95
4.9. Covariance and the behavior of error......Page 98
Problems......Page 100
5.1. When least square fails......Page 102
5.2. Prior information......Page 103
5.3. Bayesian inference......Page 105
5.4. The product of Normal probability density distributions......Page 107
5.5. Generalized least squares......Page 109
5.6. The role of the covariance of the data......Page 111
5.7. Smoothness as prior information......Page 112
5.8. Sparse matrices......Page 114
5.9. Reorganizing grids of model parameters......Page 117
Problems......Page 120
6.1. Describing sinusoidal oscillations......Page 122
6.2. Models composed only of sinusoidal functions......Page 124
6.3. Going complex......Page 131
6.4. Lessons learned from the integral transform......Page 133
6.5. Normal curve......Page 134
6.6. Spikes......Page 135
6.8. Time-delayed function......Page 137
6.10. Integral of a function......Page 139
6.11. Convolution......Page 140
6.12. Nontransient signals......Page 141
Problems......Page 143
7.1. Behavior sensitive to past conditions......Page 146
7.2. Filtering as convolution......Page 150
7.3. Solving problems with filters......Page 151
7.4. Predicting the future......Page 158
7.5. A parallel between filters and polynomials......Page 159
7.6. Filter cascades and inverse filters......Page 161
7.7. Making use of what you know......Page 164
Problems......Page 166
8.1. Samples as mixtures......Page 168
8.2. Determining the minimum number of factors......Page 170
8.3. Application to the Atlantic Rocks dataset......Page 174
8.4. Spiky factors......Page 175
8.5. Time-Variable functions......Page 179
Problems......Page 182
9.1. Correlation is covariance......Page 186
9.3. Relationship to convolution and power spectral density......Page 192
9.4. Cross-correlation......Page 193
9.5. Using the cross-correlation to align time series......Page 195
9.6. Least squares estimation of filters......Page 197
9.7. The effect of smoothing on time series......Page 199
9.8. Band-pass filters......Page 203
9.9. Frequency-dependent coherence......Page 207
9.10. Windowing before computing Fourier transforms......Page 214
9.11. Optimal window functions......Page 215
Problems......Page 220
10.1. Interpolation requires prior information......Page 222
10.2. Linear interpolation......Page 224
10.3. Cubic interpolation......Page 225
10.4. Kriging......Page 227
10.5. Interpolation in two-dimensions......Page 229
10.6. Fourier transforms in two dimensions......Page 232
Problems......Page 234
11.1. The difference is due to random variation!......Page 236
11.2. The distribution of the total error......Page 237
11.3. Four important probability density functions......Page 239
11.4. A hypothesis testing scenario......Page 241
11.5. Testing improvement in fit......Page 247
11.6. Testing the significance of a spectral peak......Page 248
11.7. Bootstrap confidence intervals......Page 253
Problems......Page 257
Note 1.1. On the persistence of MatLab variables......Page 258
Note 2.1. On time......Page 259
Note 2.2. On reading complicated text files......Page 260
Note 3.2. On the eda_draw() function......Page 261
Note 4.1. On complex least squares......Page 262
Note 5.2. On MatLab functions......Page 264
Note 6.2. On the orthonormality of the discrete Fourier data kernel......Page 265
Note 8.1. On singular value decomposition......Page 266
Note 9.1. On coherence......Page 267
Note 9.2. On Lagrange multipliers......Page 268
Index......Page 270