Dedication
Preface
Advice on scripting for beginners
1. Data analysis with MatLab
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. To loop or not to loop
1.10. The matrix inverse
1.11. Loading data from a file
1.12. Plotting data
1.13. Saving data to a file
1.14. Some advice on writing scripts
2. A first look at data
2.1. Look at your data!
2.2. More on MatLab graphics
2.3. Rate information
2.4. Scatter plots and their limitations
3. Probability and what it has to do with data analysis
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
4. The power of linear models
4.1. Quantitative models, data, and model parameters
4.2. The simplest of quantitative models
4.3. Curve fitting
4.4. Mixtures
4.5. Weighted averages
4.6. Examining error
4.7. Least squares
4.8. Examples
4.9. Covariance and the behavior of error
5. Quantifying preconceptions
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
6. Detecting periodicities
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
7. The past influences the present
7.1. Behavior sensitive to past conditions
7.2. Filtering as convolution
7.3. Solving problems with filters
7.4. Predicting the future
7.5. A parallel between filters and polynomials
7.6. Filter cascades and inverse filters
7.7. Making use of what you know
8. Patterns suggested by data
8.1. Samples as mixtures
8.2. Determining the minimum number of factors
8.3. Application to the Atlantic Rocks dataset
8.4. Spiky factors
8.5. Time-Variable functions
9. Detecting correlations among data
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
10. Filling in missing data
10.1. Interpolation requires prior information
10.2. Linear interpolation
10.3. Cubic interpolation
10.4. Kriging
10.5. Interpolation in two-dimensions
10.6. Fourier transforms in two dimensions
11. Are my results significant?
11.1. The difference is due to random variation!
11.2. The distribution of the total error
11.3. Four important probability density functions
11.4. A hypothesis testing scenario
11.5. Testing improvement in fit
11.6. Testing the significance of a spectral peak
11.7. Bootstrap confidence intervals
12. Notes
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 MatLabatan2() function
Note 6.2. On the orthonormality of the discrete Fourier data kernel
Note 8.1. On singular value decomposition
Note 9.1. On coherence
Note 9.2. On Lagrange multipliers
Index
