Environmental Data Analysis with MatLab
- 1st Edition - October 13, 2009
- Authors: William Menke, Joshua Menke
- Language: English
- eBook ISBN:9 7 8 - 0 - 1 2 - 3 9 1 8 8 7 - 1
Environmental Data Analysis with MatLab is a reference work designed to teach students and researchers the basics of data analysis in the environmental sciences using MatLab, a… Read more
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Environmental Data Analysis with MatLab is a reference work designed to teach students and researchers the basics of data analysis in the environmental sciences using MatLab, and more specifically how to analyze data sets in carefully chosen, realistic scenarios. Although written in a self-contained way, the text is supplemented with data sets and MatLab scripts that can be used as a data analysis tutorial, available at the author's website: http://www.ldeo.columbia.edu/users/menke/edawm/index.htm.
This book is organized into 12 chapters. After introducing the reader to the basics of data analysis with MatLab, the discussion turns to the power of linear models; quantifying preconceptions; detecting periodicities; patterns suggested by data; detecting correlations among the data; filling in missing data; and determining whether your results are significant. Homework problems help users follow up upon case studies.
This text will appeal to environmental scientists, specialists, researchers, analysts, and undergraduate and graduate students in Environmental Engineering, Environmental Biology and Earth Science courses, who are working to analyze data and communicate results.
- 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
Environmental scientists, specialists, researchers, analysts, undergraduate and graduate students in Environmental Engineering, Environmental Biology and Earth Science, who are working to analyze data and communicate results.
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
- Edition: 1
- Published: October 13, 2009
- Language: English
WM
William Menke
William Menke is a Professor of Earth and Environmental Sciences at Columbia University. His research focuses on the development of data analysis algorithms for time series analysis and imaging in the earth and environmental sciences and the application of these methods to volcanoes, earthquakes, and other natural hazards. He has thirty years of experience teaching data analysis methods to both undergraduates and graduate students. Relevant courses that he has taught include, at the undergraduate level, Environmental Data Analysis and The Earth System, and at the graduate level, Geophysical Inverse Theory, Quantitative Methods of Data Analysis, Geophysical Theory and Practical Seismology.
Affiliations and expertise
Professor of Earth and Environmental Sciences ,Columbia UniversityJM
Joshua Menke
Joshua Menke is a software engineer and principal of JOM Associates. His specialty is in the design and implementation of parallel processing systems for matching and correlation of large volumes of data in order to identify and quantify trends and patterns that can assist manufacturers and retailer better serve their clientele.
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