## Case Studies in Neural Data Analysis

by Kramer, Eden

### Instructor Requests

As neural data becomes increasingly complex, neuroscientists now require skills in computer programming, statistics, and data analysis. This book teaches practical neural data analysis techniques by presenting example datasets and developing techniques and tools for analyzing them. Each chapter begins with a specific example of neural data, which motivates mathematical and statistical analysis methods that are then applied to the data. This practical, hands-on approach is unique among data analysis textbooks and guides, and equips the reader with the tools necessary for real-world neural data analysis.

The book begins with an introduction to MATLAB, the most common programming platform in neuroscience, which is used in the book. (Readers familiar with MATLAB can skip this chapter and might decide to focus on data type or method type.) The book goes on to cover neural field data and spike train data, spectral analysis, generalized linear models, coherence, and cross-frequency coupling. Each chapter offers a stand-alone case study that can be used separately as part of a targeted investigation. The book includes some mathematical discussion but does not focus on mathematical or statistical theory, emphasizing the practical instead. References are included for readers who want to explore the theoretical more deeply. The data and accompanying MATLAB code are freely available on the authorsâ€™ website. The book can be used for upper-level undergraduate or graduate courses or as a professional reference.

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Contents (pg. vii)
Preface (pg. xiii)
1 Introduction to MATLAB (pg. 1)
Synopsis (pg. 1)
1.1 Introduction (pg. 1)
1.2 Starting MATLAB (pg. 1)
1.3 MATLAB Is a Calculator (pg. 2)
1.4 MATLAB Can Compute Complicated Quantities (pg. 2)
1.5 Built-in Functions (pg. 2)
1.6 Vectors (pg. 3)
1.7 Manipulating Vectors with Scalars (pg. 3)
1.8 Manipulating Vectors with Vectors (pg. 3)
1.9 Defining Variables (pg. 4)
1.10 Probing the Defined Variables (pg. 5)
1.11 Summing Elements in a Vector (pg. 5)
1.12 Clearing All Variables (pg. 6)
1.13 Matrices (pg. 6)
1.14 Indexing Matrices and Vectors (pg. 7)
1.15 Finding Subsets of Elements in Matrices and Vectors (pg. 8)
1.16 Plotting Data (pg. 9)
1.17 Multiple Plots, One atop the Other (pg. 11)
1.18 Random Numbers (pg. 11)
1.19 Histograms (pg. 13)
1.20 Repeating Commands (pg. 15)
1.21 Defining a New Function: The m-File (pg. 16)
1.22 Saving Your Work (pg. 19)
2 The Event-Related Potential from a Scalp Electroencephalogram (pg. 21)
Synopsis (pg. 21)
2.1 Introduction (pg. 21)
2.2 Data Analysis (pg. 23)
Summary (pg. 42)
Problems (pg. 42)
Appendix: Standard Error of the Mean (pg. 45)
3 Analysis of Rhythmic Activity in the Scalp Electroencephalogram (pg. 49)
Synopsis (pg. 49)
3.1 Introduction (pg. 49)
3.2 Data Analysis (pg. 50)
Summary (pg. 80)
Problems (pg. 80)
Appendix A: The Spectrum and Autocovariance (pg. 83)
Appendix B: Aliasing (pg. 85)
Appendix C: Numerical Scaling of the Spectrum (pg. 88)
4 Analysis of Rhythmic Activity in an Invasive Electrocorticogram (pg. 93)
Synopsis (pg. 93)
4.1 Introduction (pg. 93)
4.2 Data Analysis (pg. 94)
Summary (pg. 117)
Problems (pg. 117)
Appendix: Multiplication and Convolution in Different Domains (pg. 120)
5 Analysis of Coupled Rhythms in an Invasive Electrocorticogram (pg. 123)
Synopsis (pg. 123)
5.1 Introduction (pg. 123)
5.2 Data Analysis (pg. 124)
Summary (pg. 148)
Problems (pg. 150)
6 Application of Filtering to Scalp Electroencephalogram Data (pg. 155)
Synopsis (pg. 155)
6.1 Introduction (pg. 155)
6.2 Data Analysis (pg. 156)
Summary (pg. 190)
Problems (pg. 191)
7 Investigation of Cross-Frequency Coupling in a Local Field Potential (pg. 195)
Synopsis (pg. 195)
7.1 Introduction (pg. 195)
7.2 Data Analysis (pg. 196)
Summary (pg. 212)
Problems (pg. 212)
Appendix: Hilbert Transform in the Time Domain (pg. 214)
8 Basic Visualizations and Descriptive Statistics of Spike Train Data (pg. 217)
Synopsis (pg. 217)
8.1 Introduction (pg. 217)
8.2 Data Analysis (pg. 218)
Summary (pg. 259)
Problems (pg. 260)
Appendix: Spike Count Mean and Variance for a Poisson Process (pg. 262)
9 Modeling Place Fields with Point Process GeneralizedLinear Models (pg. 265)
Synopsis (pg. 265)
9.1 Introduction (pg. 265)
9.2 Data Analysis (pg. 266)
Summary (pg. 296)
Problems (pg. 297)
10 Analysis of Rhythmic Spiking in the Subthalamic Nucleus during a Movement Task (pg. 299)
Synopsis (pg. 299)
10.1 Introduction (pg. 299)
10.2 Data Analysis (pg. 300)
Summary (pg. 340)
Problems (pg. 341)
11 Analysis of Spike-Field Coherence during Navigation (pg. 343)
Synopsis (pg. 343)
11.1 Introduction (pg. 343)
11.2 Data Analysis (pg. 344)
Summary (pg. 361)
Problems (pg. 361)
References (pg. 365)
Index (pg. 367)

#### Mark A. Kramer

Mark A. Kramer is Associate Professor in the Department of Mathematics and Statistics at Boston University.

#### Uri T. Eden

Uri T. Eden is Associate Professor in the Department of Mathematics and Statistics at Boston University.

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