Table of Contents
1.2 Getting started with MatLab
1.5 Simple arithmetic and algebra
1.7 Multiplication of vectors of matrices
1.15 Some advice on writing scripts
2.4 Scatter plots and their limitations
3: Probability and what it has to do with data analysis
3.4 Two important probability density functions
3.5 Functions of a random variable
3.8 Joint probability density functions
3.10 Multivariate distributions
3.11 The multivariate Normal distributions
3.12 Linear functions of multivariate data
4.1 Quantitative models, data, and model parameters
4.2 The simplest of quantitative models
4.9 Covariance and the behavior of error
5.4 The product of Normal probability density distributions
5.6 The role of the covariance of the data
5.7 Smoothness as prior information
5.9 Reorganizing grids of model parameters
6.1 Describing sinusoidal oscillations
6.2 Models composed only of sinusoidal functions
6.4 Lessons learned from the integral transform
7: The past influences the present
7.1 Behavior sensitive to past conditions
7.3 Solving problems with filters
7.4 An example of an empirically-derived filter
7.6 A parallel between filters and polynomials
7.7 Filter cascades and inverse filters
7.8 Making use of what you know
8.2 Determining the minimum number of factors
8.3 Application to the Atlantic Rocks dataset
8.6 Q-mode factor analysis and spatial clustering
9: Detecting correlations among data
9.2 Computing autocorrelation by hand
9.3 Relationship to convolution and power spectral density
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
9.9 Frequency-dependent coherence
9.10 Windowing before computing Fourier transforms
10.1 Interpolation requires prior information
10.5 Interpolation in two-dimensions
10.6 Fourier transforms in two dimensions
11: “Approximate” is not a pejorative word
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
11.11 Precomputation of a function and table lookups
11.12 Artificial neural networks
11.13 Information flow in a neural net
11.15 Neural net for a nonlinear response
12: Are my results significant?
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
Note 1.1 On the persistence of MatLab variables
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 5.3 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