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Environmental Data Analysis with MatLab

Book Description

Environmental Data Analysis with MatLab is for students and researchers working to analyze real data sets in the environmental sciences. One only has to consider the global warming debate to realize how critically important it is to be able to derive clear conclusions from often-noisy data drawn from a broad range of sources. This book teaches the basics of the underlying theory of data analysis, and then reinforces that knowledge with carefully chosen, realistic scenarios. MatLab, a commercial data processing environment, is used in these scenarios; significant content is devoted to teaching how it can be effectively used in an environmental data analysis setting. The book, though written in a self-contained way, is supplemented with data sets and MatLab scripts that can be used as a data analysis tutorial.



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

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