- Cover image
- Title page
- Table of Contents
- Copyright
- Dedication
- Preface
- Advice on scripting for beginners
- 1: Data analysis with MatLab
- Abstract
- 1.1 Why MatLab?
- 1.2 Getting started with MatLab
- 1.3 Getting organized
- 1.4 Navigating folders
- 1.5 Simple arithmetic and algebra
- 1.6 Vectors and matrices
- 1.7 Multiplication of vectors of matrices
- 1.8 Element access
- 1.9 Representing functions
- 1.10 To loop or not to loop
- 1.11 The matrix inverse
- 1.12 Loading data from a file
- 1.13 Plotting data
- 1.14 Saving data to a file
- 1.15 Some advice on writing scripts
- Problems
- 2: A first look at data
- 3: Probability and what it has to do with data analysis
- Abstract
- 3.1 Random variables
- 3.2 Mean, median, and mode
- 3.3 Variance
- 3.4 Two important probability density functions
- 3.5 Functions of a random variable
- 3.6 Joint probabilities
- 3.7 Bayesian inference
- 3.8 Joint probability density functions
- 3.9 Covariance
- 3.10 Multivariate distributions
- 3.11 The multivariate Normal distributions
- 3.12 Linear functions of multivariate data
- Problems
- 4: The power of linear models
- 5: Quantifying preconceptions
- Abstract
- 5.1 When least square fails
- 5.2 Prior information
- 5.3 Bayesian inference
- 5.4 The product of Normal probability density distributions
- 5.5 Generalized least squares
- 5.6 The role of the covariance of the data
- 5.7 Smoothness as prior information
- 5.8 Sparse matrices
- 5.9 Reorganizing grids of model parameters
- Problems
- 6: Detecting periodicities
- Abstract
- 6.1 Describing sinusoidal oscillations
- 6.2 Models composed only of sinusoidal functions
- 6.3 Going complex
- 6.4 Lessons learned from the integral transform
- 6.5 Normal curve
- 6.6 Spikes
- 6.7 Area under a function
- 6.8 Time-delayed function
- 6.9 Derivative of a function
- 6.10 Integral of a function
- 6.11 Convolution
- 6.12 Nontransient signals
- Problems
- 7: The past influences the present
- Abstract
- 7.1 Behavior sensitive to past conditions
- 7.2 Filtering as convolution
- 7.3 Solving problems with filters
- 7.4 An example of an empirically-derived filter
- 7.5 Predicting the future
- 7.6 A parallel between filters and polynomials
- 7.7 Filter cascades and inverse filters
- 7.8 Making use of what you know
- Problems
- 8: Patterns suggested by data
- 9: Detecting correlations among data
- Abstract
- 9.1 Correlation is covariance
- 9.2 Computing autocorrelation by hand
- 9.3 Relationship to convolution and power spectral density
- 9.4 Cross-correlation
- 9.5 Using the cross-correlation to align time series
- 9.6 Least squares estimation of filters
- 9.7 The effect of smoothing on time series
- 9.8 Band-pass filters
- 9.9 Frequency-dependent coherence
- 9.10 Windowing before computing Fourier transforms
- 9.11 Optimal window functions
- Problems
- 10: Filling in missing data
- 11: “Approximate” is not a pejorative word
- Abstract
- 11.1 The value of approximation
- 11.2 Polynomial approximations and Taylor series
- 11.3 Small number approximations
- 11.4 Small number approximation applied to distance on a sphere
- 11.5 Small number approximation applied to variance
- 11.6 Taylor series in multiple dimensions
- 11.7 Small number approximation applied to covariance
- 11.8 Solving nonlinear problems with iterative least squares
- 11.9 Fitting a sinusoid of unknown frequency
- 11.10 The gradient method
- 11.11 Precomputation of a function and table lookups
- 11.12 Artificial neural networks
- 11.13 Information flow in a neural net
- 11.14 Training a neural net
- 11.15 Neural net for a nonlinear response
- Problems
- 12: Are my results significant?
- Abstract
- 12.1 The difference is due to random variation!
- 12.2 The distribution of the total error
- 12.3 Four important probability density functions
- 12.4 A hypothesis testing scenario
- 12.5 Chi-squared test for generalized least squares
- 12.6 Testing improvement in fit
- 12.7 Testing the significance of a spectral peak
- 12.8 Bootstrap confidence intervals
- Problems
- 13: Notes
- Abstract
- Note 1.1 On the persistence of MatLab variables
- Note 2.1 On time
- Note 2.2 On reading complicated text files
- Note 3.1 On the rule for error propagation
- Note 3.2 On the eda_draw() function
- Note 4.1 On complex least squares
- Note 5.1 On the derivation of generalized least squares
- Note 5.2 On MatLab functions
- Note 5.3 On reorganizing matrices
- Note 6.1 On the MatLab atan2() function
- Note 6.2 On the orthonormality of the discrete Fourier data kernel
- Note 6.3 On the expansion of a function in an orthonormal basis
- Note 8.1 On singular value decomposition
- Note 9.1 On coherence
- Note 9.2 On Lagrange multipliers
- Note 11.1 On the chain rule for partial derivatives
- Index
Environmental Data Analysis with MATLAB®
Second Edition
William Menke
Professor of Earth and Environmental Sciences, Columbia University
Joshua Menke
Software Engineer, JOM Associates
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