Analyzing neural time series data : theory and practice / Mike X. Cohen.

Includes bibliographies and index.

"This book offers a comprehensive guide to the theory and practice of analyzing electrical brain signals. It explains the conceptual, mathematical, and implementational (via Matlab programming) aspects of time-, time-frequency- and synchronization-based analyses of magnetoencephalography (MEG), electroencephalography (EEG), and local field potential (LFP) recordings from humans and nonhuman animals. It is the only book on the topic that covers both the theoretical background and the implementation in language that can be understood by readers without extensive formal training in mathematics, including cognitive scientists, neuroscientists, and psychologists."--

part I Introduction -- 1. The Purpose of This Book, Who Should Read It, and How to Use It -- 1.1. What Is Cognitive Electrophysiology? -- 1.2. What Is the Purpose of This Book? -- 1.3. Why Shouldn't You Use <Insert Name of M/EEG Software Analysis Package>? -- 1.4. Why Program Analyses, and Why in Matlab? -- 1.5. How Best to Learn from and Use This Book -- 1.6. Sample Data and Online Code -- 1.7. Terminology Used in This Book -- 1.8. Exercises -- 1.9. Is Everything There Is to Know about EEG Analyses in This Book? -- 1.10. Who Should Read This Book? -- 1.11. Is This Book Difficult? -- 1.12. Questions? -- 2. Advantages and Limitations of Time and Time-Frequency-Domain Analyses -- 2.1. Why EEG? -- 2.2. Why Not EEG? -- 2.3. Interpreting Voltage Values from the EEG Signal -- 2.4. Advantages of Event-Related Potentials -- 2.5. Limitations of ERPs -- 2.6. Advantages of Time-Frequency-Based Approaches -- 2.7. Limitations of Time-Frequency-Based Approaches.

2.8. Temporal Resolution, Precision, and Accuracy of EEG -- 2.9. Spatial Resolution, Precision, and Accuracy of EEG -- 2.10. Topographical Localization versus Brain Localization -- 2.11. EEG or MEG? -- 2.12. Costs of EEG Research -- 3. Interpreting and Asking Questions about Time-Frequency Results -- 3.1. EEG Time-Frequency: The Basics -- 3.2. Ways to View Time-Frequency Results -- 3.3. Tfviewerx and erpviewerx -- 3.4. How to View and Interpret Time-Frequency Results -- 3.5. Things to Be Suspicious of When Viewing Time-Frequency Results -- 3.6. Do Results in Time-Frequency Plots Mean That There Were Neural Oscillations? -- 4. Introduction to Matlab Programming -- 4.1. Write Clean and Efficient Code -- 4.2. Use Meaningful File and Variable Names -- 4.3. Make Regular Backups of Your Code and Keep Original Copies of Modified Code -- 4.4. Initialize Variables -- 4.5. Help! -- 4.6. Be Patient and Embrace the Learning Experience -- 4.7. Exercises.

5. Introduction to the Physiological Bases of EEG -- 5.1. Biophysical Events That Are Measurable with EEG -- 5.2. Neurobiological Mechanisms of Oscillations -- 5.3. Phase-Locked, Time-Locked, Task-Related -- 5.4. Neurophysiological Mechanisms of ERPs -- 5.5. Are Electrical Fields Causally Involved in Cognition? -- 5.6. What if Electrical Fields Are Not Causally Involved in Cognition? -- 6. Practicalities of EEG Measurement and Experiment Design -- 6.1. Designing Experiments: Discuss, Pilot, Discuss, Pilot -- 6.2. Event Markers -- 6.3. Intra- and Intertrial Timing -- 6.4. How Many Trials You Will Need -- 6.5. How Many Electrodes You Will Need -- 6.6. Which Sampling Rate to Use When Recording Data -- 6.7. Other Optional Equipment to Consider -- part II Preprocessing and Time-Domain Analyses -- 7. Preprocessing Steps Necessary and Useful for Advanced Data Analysis -- 7.1. What Is Preprocessing? -- 7.2. The Balance between Signal and Noise -- 7.3. Creating Epochs.

7.4. Matching Trial Count across Conditions -- 7.5. Filtering -- 7.6. Trial Rejection -- 7.7. Spatial Filtering -- 7.8. Referencing -- 7.9. Interpolating Bad Electrodes -- 7.10. Start with Clean Data -- 8. EEG Artifacts: Their Detection, Influence, and Removal -- 8.1. Removing Data Based on Independent Components Analysis -- 8.2. Removing Trials because of Blinks -- 8.3. Removing Trials because of Oculomotor Activity -- 8.4. Removing Trials Based on EMG in EEG Channels -- 8.5. Removing Trials Based on Task Performance -- 8.6. Removing Trials Based on Response Hand EMG -- 8.7. Train Subjects to Minimize Artifacts -- 8.8. Minimize Artifacts during Data Collection -- 9. Overview of Time-Domain EEG Analyses -- 9.1. Event-Related Potentials -- 9.2. Filtering ERPs -- 9.3. Butterfly Plots and Global Field Power/Topographical Variance Plots -- 9.4. The Flicker Effect -- 9.5. Topographical Maps -- 9.6. Microstates -- 9.7. ERP Images -- 9.8. Exercises.

part III Frequency and Time-Frequency Domains Analyses -- 10. The Dot Product and Convolution -- 10.1. Dot Product -- 10.2. Convolution -- 10.3. How Does Convolution Work? -- 10.4. Convolution versus Cross-Covariance -- 10.5. The Purpose of Convolution for EEG Data Analyses -- 10.6. Exercises -- 11. The Discrete Time Fourier Transform, the FFT, and the Convolution Theorem -- 11.1. Making Waves -- 11.2. Finding Waves in EEG Data with the Fourier Transform -- 11.3. The Discrete Time Fourier Transform -- 11.4. Visualizing the Results of a Fourier Transform -- 11.5.Complex Results and Negative Frequencies -- 11.6. Inverse Fourier Transform -- 11.7. The Fast Fourier Transform -- 11.8. Stationarity and the Fourier Transform -- 11.9. Extracting More or Fewer Frequencies than Data Points -- 11.10. The Convolution Theorem -- 11.11. Tips for Performing FFT-Based Convolution in Matlab -- 11.12. Exercises -- 12. Morlet Wavelets and Wavelet Convolution -- 12.1. Why Wavelets?

12.2. How to Make Wavelets -- 12.3. Wavelet Convolution as a Bandpass Filter -- 12.4. Limitations of Wavelet Convolution as Discussed Thus Far -- 12.5. Exercises -- 13.Complex Morlet Wavelets and Extracting Power and Phase -- 13.1. The Wavelet Complex -- 13.2. Imagining the Imaginary -- 13.3. Rectangular and Polar Notation and the Complex Plane -- 13.4. Euler's Formula -- 13.5. Euler's Formula and the Result of Complex Wavelet Convolution -- 13.6. From Time Point to Time Series -- 13.7. Parameters of Wavelets and Recommended Settings -- 13.8. Determining the Frequency Smoothing of Wavelets -- 13.9. Tips for Writing Efficient Convolution Code in Matlab -- 13.10. Describing This Analysis in Your Methods Section -- 13.11. Exercises -- 14. Bandpass Filtering and the Hilbert Transform -- 14.1. Hilbert Transform -- 14.2. Filtering Data before Applying the Hilbert Transform -- 14.3. Finite versus Infinite Impulse Response Filters -- 14.4. Bandpass, Band-Stop, High-Pass, Low-Pass.

14.5. Constructing a Filter -- 14.6. Check Your Filters -- 14.7. Applying the Filter to Data -- 14.8. Butterworth (IIR) Filter -- 14.9. Filtering Each Trial versus Filtering Concatenated Trials -- 14.10. Multiple Frequencies -- 14.11.A World of Filters -- 14.12. Describing This Analysis in Your Methods Section -- 14.13. Exercises -- 15. Short-Time FFT -- 15.1. How the Short-Time FFT Works -- 15.2. Taper the Time Series -- 15.3. Time Segment Lengths and Overlap -- 15.4. Power and Phase -- 15.5. Describing This Analysis in Your Methods Section -- 15.6. Exercises -- 16. Multitapers -- 16.1. How the Multitaper Method Works -- 16.2. The Tapers -- 16.3. When You Should and Should Not Use Multitapers -- 16.4. The Multitaper Framework and Advanced Topics -- 16.5. Describing This Analysis in Your Methods Section -- 16.6. Exercises -- 17. Less Commonly Used Time-Frequency Decomposition Methods -- 17.1. Autoregressive Modeling -- 17.2. Hilbert-Huang (Empirical Mode Decomposition).

17.3. Matching Pursuit -- 17.4.P-Episode -- 17.5.S-Transform -- 18. Time-Frequency Power and Baseline Normalizations -- 18.1.1/f Power Scaling -- 18.2. The Solution to 1/f Power in Task Designs -- 18.3. Decibel Conversion -- 18.4. Percentage Change and Baseline Division -- 18.5.Z-Transform -- 18.6. Not All Transforms Are Equal -- 18.7. Other Transforms -- 18.8. Mean versus Median -- 18.9. Single-Trial Baseline Normalization -- 18.10. The Choice of Baseline Time Window -- 18.11. Disadvantages of Baseline-Normalized Power -- 18.12. Signal-to-Noise Estimates -- 18.13. Number of Trials and Power Estimates -- 18.14. Downsampling Results after Analyses -- 18.15. Describing This Analysis in Your Methods Section -- 18.16. Exercises -- 19. Intertrial Phase Clustering -- 19.1. Why Phase Values Cannot Be Averaged -- 19.2. Intertrial Phase Clustering -- 19.3. Strength in Numbers -- 19.4. Using ITPC When There Are Few Trials or Condition Differences in Trial Count.

19.5. Effects of Temporal Jitter on ITPC and Power -- 19.6. ITPC and Power -- 19.7. Weighted ITPC -- 19.8. Multimodal Phase Distributions -- 19.9. Spike-Field Coherence -- 19.10. Describing This Analysis in Your Methods Section -- 19.11. Exercises -- 20. Differences among Total, Phase-Locked, and Non-Phase-Locked Power and Intertrial Phase Consistency -- 20.1. Total Power -- 20.2. Non-Phase-Locked Power -- 20.3. Phase-Locked Power -- 20.4. ERP Time-Frequency Power -- 20.5. Intertrial Phase Clustering -- 20.6. When to Use What Approach -- 20.7. Exercise -- 21. Interpretations and Limitations of Time-Frequency Power and ITPC Analyses -- 21.1. Terminology -- 21.2. When to Use What Time-Frequency Decomposition Method -- 21.3. Interpreting Time-Frequency Power -- 21.4. Interpreting Time-Frequency Intertrial Phase Clustering -- 21.5. Limitations of Time-Frequency Power and Intertrial Phase Clustering -- 21.6. Do Time-Frequency Analyses Reveal Neural Oscillations?

part IV Spatial Filters -- 22. Surface Laplacian -- 22.1. What Is the Surface Laplacian? -- 22.2. Algorithms for Computing the Surface Laplacian for EEG Data -- 22.3. Surface Laplacian for Topographical Localization -- 22.4. Surface Laplacian for Connectivity Analyses -- 22.5. Surface Laplacian for Cleaning Topographical Noise -- 22.6. Describing This Analysis in Your Methods Section -- 22.7. Exercises -- 23. Principal Components Analysis -- 23.1. Purpose and Interpretations of Principal Components Analysis -- 23.2. How PCA Is Computed -- 23.3. Distinguishing Significant from Nonsignificant Components -- 23.4. Rotating PCA Solutions -- 23.5. Time-Resolved PCA -- 23.6. PCA with Time-Frequency Information -- 23.7. PCA across Conditions -- 23.8. Independent Components Analysis -- 23.9. Describing This Method in Your Methods Section -- 23.10. Exercises -- 24. Basics of Single-Dipole and Distributed-Source Imaging -- 24.1. The Forward Solution -- 24.2. The Inverse Problem.

24.3. Dipole Fitting -- 24.4. Nonadaptive Distributed-Source Imaging Methods -- 24.5. Adaptive Distributed-Source Imaging -- 24.6. Theoretical and Practical Limits of Spatial Precision and Resolution -- part V Connectivity -- 25. Introduction to the Various Connectivity Analyses -- 25.1. Why Only Two Sites (Bivariate Connectivity)? -- 25.2. Important Concepts Related to Bivariate Connectivity -- 25.3. Which Measure of Connectivity Should Be Used? -- 25.4. Phase-Based Connectivity -- 25.5. Power-Based Connectivity -- 25.6. Granger Prediction -- 25.7. Mutual Information -- 25.8. Cross-Frequency Coupling -- 25.9. Graph Theory -- 25.10. Potential Confound of Volume Conduction -- 26. Phase-Based Connectivity -- 26.1. Terminology -- 26.2. ISPC over Time -- 26.3. ISPC-Trials -- 26.4. ISPC and the Number of Trials -- 26.5. Relation between ISPC and Power -- 26.6. Weighted ISPC-Trials -- 26.7. Spectral Coherence (Magnitude-Squared Coherence) -- 26.8. Phase Lag-Based Measures.

26.9. Which Measure of Phase Connectivity Should You Use? -- 26.10. Testing the Mean Phase Angle -- 26.11. Describing These Analyses in Your Methods Section -- 26.12. Exercises -- 27. Power-Based Connectivity -- 27.1. Spearman versus Pearson Coefficient for Power Correlations -- 27.2. Power Correlations over Time -- 27.3. Power Correlations over Trials -- 27.4. Partial Correlations -- 27.5. Matlab Programming Tips -- 27.6. Describing This Analysis in Your Methods Section -- 27.7. Exercises -- 28. Granger Prediction -- 28.1. Univariate Autoregression -- 28.2. Bivariate Autoregression -- 28.3. Autoregression Errors and Error Variances -- 28.4. Granger Prediction over Time -- 28.5. Model Order -- 28.6. Frequency Domain Granger Prediction -- 28.7. Time Series Covariance Stationarity -- 28.8. Baseline Normalization of Granger Prediction Results -- 28.9. Statistics -- 28.10. Additional Applications of Granger Prediction -- 28.11. Exercises -- 29. Mutual Information -- 29.1. Entropy.

29.2. How Many Histogram Bins to Use -- 29.3. Enjoy the Entropy -- 29.4. Joint Entropy -- 29.5. Mutual Information -- 29.6. Mutual Information and Amount of Data -- 29.7. Mutual Information with Noisy Data -- 29.8. Mutual Information over Time or over Trials -- 29.9. Mutual Information on Real Data -- 29.10. Mutual Information on Frequency-Band-Specific Data -- 29.11. Lagged Mutual Information -- 29.12. Statistics -- 29.13. More Information -- 29.14. Describing This Analysis in Your Methods Section -- 29.15. Exercises -- 30. Cross-Frequency Coupling -- 30.1. Visual Inspection of Cross-Frequency Coupling -- 30.2. Power-Power Correlations -- 30.3.A Priori Phase-Amplitude Coupling -- 30.4. Separating Task-Related Phase and Power Coactivations from Phase-Amplitude Coupling -- 30.5. Mixed A Priori/Exploratory Phase-Amplitude Coupling -- 30.6. Exploratory Phase-Amplitude Coupling -- 30.7. Notes about Phase-Amplitude Coupling -- 30.8. Phase-Phase Coupling.

30.9. Other Methods for Quantifying Cross-Frequency Coupling -- 30.10. Cross-Frequency Coupling over Time or over Trials -- 30.11. Describing This Analysis in Your Methods Section -- 30.12. Exercises -- 31. Graph Theory -- 31.1.Networks as Matrices and Graphs -- 31.2. Thresholding Connectivity Matrices -- 31.3. Connectivity Degree -- 31.3. Clustering Coefficient -- 31.4. Path Length -- 31.5. Small-World Networks -- 31.6. Statistics -- 31.7. How to Describe These Analyses in Your Paper -- 31.8. Exercises -- part VI Statistical Analyses -- 32. Advantages and Limitations of Different Statistical Procedures -- 32.1. Are Statistics Necessary? -- 32.2. At What Level Should Statistics Be Performed? -- 32.3. What p-Value Should Be Used, and Should Multiple-Comparisons Corrections Be Applied? -- 32.4. Are p-Values the Only Statistical Metric? -- 32.5. Statistical Significance versus Practical Significance -- 32.6. Type I and Type II Errors.

32.7. What Kinds of Statistics Should Be Applied? -- 32.8. How to Combine Data across Subjects -- 33. Nonparametric Permutation Testing -- 33.1. Advantages of Nonparametric Permutation Testing -- 33.2. Creating a Null-Hypothesis Distribution -- 33.3. How Many Iterations Are Necessary for the Null-Hypothesis Distribution? -- 33.4. Determining Statistical Significance -- 33.5. Multiple Comparisons and Their Corrections -- 33.6. Correction for Multiple Comparisons Using Pixel-Based Statistics -- 33.7. Corrections for Multiple Comparisons Using Cluster-Based Statistics -- 33.8. False Discovery Rate for Multiple-Comparisons Correction -- 33.9. What Should Be Permuted? -- 33.10. Nonparametric Permutation Testing beyond Simple Bivariate Cases -- 33.11. Describing This Analysis in Your Methods Section -- 34. Within-Subject Statistical Analyses -- 34.1. Changes in Task-Related Power Compared to Baseline -- 34.2. Discrete Condition Differences in Power.

34.3. Continuous Relationship with Power: Single-Trial Correlations -- 34.4. Continuous Relationships with Power: Single-Trial Multiple Regression -- 34.5. Determining Statistical Significance of Phase-Based Data -- 34.6. Testing Preferred Phase Angle across Conditions -- 34.7. Testing the Statistical Significance of Correlation Coefficients -- 35. Group-Level Analyses -- 35.1. Avoid Circular Inferences -- 35.2. Group-Level Analysis Strategy 1: Test Each Pixel and Apply a Mapwise Threshold -- 35.3. Group-Level Analysis Strategy 2a: Time-Frequency Windows for Hypothesis-Driven Analyses -- 35.4. Group-Level Analysis Strategy 2b: Subject-Specific Time-Frequency Windows for Hypothesis-Driven Analyses -- 35.5. Determining How Many Subjects You Need for Group-Level Analyses -- 36. Recommendations for Reporting Results in Figures, Tables, and Text -- 36.1. Recommendation 1: One Figure, One Idea -- 36.2. Recommendation 2: Show Data.

36.3. Recommendation 3: Highlight Significant Effects Instead of Removing Nonsignificant Effects -- 36.4. Recommendation 4: Show Specificity (or Lack Thereof) in Frequency, Time, and Space -- 36.5. Recommendation 5: Use Color -- 36.6. Recommendation 6: Use Informative Figure Labels and Captions -- 36.7. Recommendation 7: Avoid Showing "Representative" Data -- 36.8.A Checklist for Making Figures -- 36.9. Tables -- 36.10. Reporting Results in the Results Section -- part VII Conclusions and Future Directions -- 37. Recurring Themes in This Book and Some Personal Advice -- 37.1. Theme: Myriad Possible Analyses -- 37.2. Advice: Avoid the Paralysis of Analysis -- 37.3. Theme: You Don't Have to Program Your Own Analyses, but You Should Know How Analyses Work -- 37.4. Advice: If It Feels Wrong, It Probably Is -- 37.5. Advice: When in Doubt, Plot It Out -- 37.6. Advice: Know These Three Formulas like the Back of Your Hand -- 37.7. Theme: Connectivity over Trials or over Time.

37.8. Theme: Most Analysis Parameters Introduce Bias -- 37.9. Theme: Write a Clear Methods Section so Others Can Replicate Your Analyses -- 37.10. Theme: Use Descriptive and Appropriate Analysis Terms -- 37.11. Advice: Interpret Null Results Cautiously -- 37.12. Advice: Try Simulations but Also Trust Real Data -- 37.13. Advice: Trust Replications -- 37.14. Theme: Analyses Are Not Right or Wrong; They Are Appropriate or Inappropriate -- 37.15. Advice: Hypothesis Testing Is Good/Bad, and So Is Data-Driven Exploration -- 37.16. Advice: Find Something That Drives You and Study It -- 37.17. Cognitive Electrophysiology: The Art of Finding Anthills on Mountains -- 38. The Future of Cognitive Electrophysiology -- 38.1. Developments in Analysis Methods -- 38.2. Developments in Understanding the Neurophysiology of EEG -- 38.3. Developments in Experiment Design -- 38.4. Developments in Measurement Technology -- 38.5. The Role of the Body in Brain Function.

38.6. Determining Causality -- 38.7. Inferring Cognitive States from EEG Signatures: Inverse Inference -- 38.8. Tables of Activation -- 38.9. Disease Diagnosis and Predicting Treatment Course and Success -- 38.10. Clinical Relevance Is Not Necessary for the Advancement of Science -- 38.11. Replications -- 38.12. Double-Blind Review for Scientific Publications -- 38.13.?

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