ENVIRONMENTAL DATA ANALYSIS WILLIAM MENKE JOSHUA MENKE WITH MATLAB COPYRIGHT 2011 BY ELSEVIER, INC. ALL RIGHTS RESERVED.
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1 ENVIRONMENTAL DATA ANALYSIS WITH MATLAB WILLIAM MENKE PROFESSOR OF EARTH AND ENVIRONMENTAL SCIENCE COLUMBIA UNIVERSITY JOSHUA MENKE SOFTWARE ENGINEER JOM ASSOCIATES COPYRIGHT 2011 BY ELSEVIER, INC. ALL RIGHTS RESERVED.
2 CONTENTS CHAPTER 1: DATA ANALYSIS WITH MATLAB SECTION 1.1 WHY MATLAB? SECTION 1.2 GETTING STARTED WITH MATLAB. SECTION 1.3 GETTING ORGANIZED. SECTION 1.4 NAVIGATING FOLDERS. SECTION 1.5 SIMPLE ARITHMETIC AND ALGEGRA. SECTION 1.6 VECTORS AND MATRICES. SECTION 1.7 MULTIPLICATION OF VECTORS OF MATRICES SECTION 1.8 ELEMENT ACCESS. SECTION 1.9 TO LOOP OR NOT TO LOOP. SECTION 1.10 THE MATRIX INVERSE. SECTION 1.11 LOADING DATA FROM A FILE SECTION 1.12 PLOTTING DATA. SECTION 1.13 SAVING DATA TO A FILE. SECTION 1.14 SOME ADVICE ON WRITING SCRIPTS CHAPTER 2: A FIRST LOOK AT DATA SECTION 2.1 LOOK AT YOUR DATA! SECTION 2.2 MORE ON MATLAB GRAPHICS. SECTION 2.3 RATE INFORMATION. SECTION 2.4 SCATTER PLOTS AND THEIR LIMITATIONS CHAPTER 3: PROBABILITY AND WHAT IT HAS TO DO WITH DATA ANALYSIS SECTION 3.1 RANDOM VARIABLES. SECTION 3.2 MEAN, MEDIAN AND MODE. SECTION 3.3 VARIANCE. SECTION 3.4 TWO IMPORTANT PROBABILITY DENSITY FUNCTIONS SECTION 3.5 FUNCTIONS OF A RANDOM VARIABLE. SECTION 3.6 JOINT PROBABILITIES. SECTION 3.7 BAYESIAN INFERENCE SECTION 3.8 JOINT PROBABILITY DENSITY FUNCTIONS.
3 SECTION 3.9 COVARIANCE. SECTION 3.10 MULTIVARIATE DISTRIUBUTIONS. SECTION 3.11 THE MULTIVARIATE NORMAL DISTRIUBUTIONS. SECTION 3.12 LINEAR FUNCTIONS OF MULTIVATIATE DATA CHAPTER 4: THE POWER OF LINEAR MODELS SECTION 4.1 QUANTITATIVE MODELS, DATA AND MODEL PARAMETERS. SECTION 4.2 THE SIMPLEST OF QUANTITATIVE MODELS SECTION 4.3 CURVE FITTING SECTION 4.4. MIXTURES. SECTION 4.5. WEIGHTED AVERAGES. SECTION 4.6. EXAMINING ERROR. SECTION 4.7. LEAST SQUARES. SECTION 4.8. EXAMPLES. SECTION 4.9. COVARIANCE AND THE BEHAVIOR OF ERROR. CHAPTER 5:QUANTIFYING PRECONCEPTIONS SECTION 5.1 WHEN LEAST-SQUARE FAILS. SECTION 5.2 PRIOR INFORMATION. SECTION 5.3 BAYESIAN INFERENCE SECTION 5.4 THE PRODUCT OF NORMAL PROBABILITY DENSITY DISTRIBUTIONS. SECTION 5.5 GENERALIZED LEAST SQUARES. SECTION 5.6 THE ROLE OF THE COVARIANCE OF THE DATA SECTION 5.7. SMOOTHNESS AS PRIOR INFORMATION. SECTION 5.8. SPARSE MATRICES. SECTION 5.9 REORGANIZING GRIDS OF MODEL PARAMETERS CHAPTER 6: DETECTING PERIODICITIES SECTION 6.1 DESCRIBING SINUSOIDAL OSCILLATIONS SECTION 6.2 MODELS COMPOSED ONLY OF HARMONIC FUNCTIONS. SECTION 6.3 GOING COMPLEX SECTION 6.4 LESSONS LEARNED FROM THE INTEGRAL TRANSFORM SECTION 6.5. NORMAL CURVE. SECTION 6.6. SPIKES.
4 SECTION 6.7. AREA UNDER A FUNCTION. SECTION 6.8. TIME-DELAYED FUNCTION. SECTION 6.9. DERIVATIVE OF A FUNCTION. SECTION INTEGRAL OF A FUNCTION SECTION CONVOLUTION. SECTION NON-TRANSIENT SIGNALS. CHAPTER 7: THE PAST INFLUENCES THE PRESENT SECTION 7.1 BEHAVIOR SENSITIVE TO PAST CONDITIONS. SECTION 7.2 FILTERING AS CONVOLUTION. SECTION 7.3 SOLVING PROBLEMS WITH FILTERS. SECTION 7.4 PREDICTION THE FUTURE SECTION 7.5 A PARALLEL BETWEEN FILTERS AND POLYNOMIALS SECTION 7.6 FILTER CASCADES AND INVERSE FILTERS SECTION 7.7 MAKING USE OF WHAT YOU KNOW. CHAPTER 8: PATTERNS SUGGESTED BY DATA SECTION 8.1 SAMPLES AS MIXTURES. SECTION 8.2 DETERMINING THE MINIMUM NUMBER OF FACTORS. SECTION 8.3. APPLICATION TO THE ATLANTIC ROCKS DATASET SECTION 8.4. SPIKY FACTORS SECTION 8.5. TIME-VARIABLE FUNCTIONS. CHAPTER 9: DETECTING CORRELATIONS AMONG DATA SECTION 9.1 CORRELATION IS COVARIANCE SECTION 9.2 COMPUTING AUTOCORRELATION BY HAND. SECTION 9.3 RELATIONSHIP TO CONVOLUTION AND POWER SPECTRAL DENSITY. SECTION 9.4. CROSS-CORRELATION. SECTION 9.5. USING THE CROSS-CORRELATION TO ALIGN TIME SERIES. SECTION 9.6 LEAST SQUARES ESTIMATION OF FILTERS SECTION 9.7. THE EFFECT OF SMOOTHING ON TIME SERIES. SECTION 9.8. BAND-PASS FILTERS. SECTION 9.9. FREQUENCY-DEPENDENT COHERENCE SECTION WINDOWING BEFORE COMPUTING FOURIER TRANSFORMS.
5 SECTION OPTIMAL WINDOW FUNCTIONS CHAPTER 10: FILLING IN MISSING DATA SECTION 10.1 INTERPOLATION REQUIRES PRIOR INFORMATION. SECTION 10.2 LINEAR INTERPOLATION SECTION 10.3 CUBIC INTERPOLATION SECTION 10.4 KRIGING SECTION 10.5 INTERPOLATION IN TWO DIMENSIONS SECTION FOURIER TRANSFORMS IN TWO DIMENSIONS. CHAPTER 11: ARE MY RESULTS SIGNIFICANT? SECTION 11.1 THE DIFFERENCE IS DUE TO RANDOM VARIATION! SECTION THE DISTRIBUTION OF THE TOTAL ERROR. SECTION FOUR IMPORTANT PROBABILITY DENSITY FUNCTIONS. SECTION A HYPOTHESIS TESTING SCENARIO. SECTION TESTING IMPROVEMENT IN FIT. SECTION TESTING THE SIGNIFICANCE OF A SPECTRAL PEAK SECTION BOOTSTRAP CONFIDENCE INTERVALS. CHAPTER 12: NOTES
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