Durstewitz Daniel. Advanced Data Analysis in Neuroscience: Integrating Statistical and Computational Models

Springer, 2017. — 292 p. — ISBN: 978-3319599748This book is intended for use in advanced graduate courses in statistics / machine learning, as well as for all experimental neuroscientists seeking to understand statistical methods at a deeper level, and theoretical neuroscientists with a limited background in statistics. It reviews almost all areas of applied statistics, from basic statistical estimation and test theory, linear and nonlinear approaches for regression and classification, to model selection and methods for dimensionality reduction, density estimation and unsupervised clustering. Its focus, however, is linear and nonlinear time series analysis from a dynamical systems perspective, based on which it aims to convey an understanding also of the dynamical mechanisms that could have generated observed time series. Further, it integrates computational modeling of behavioral and neural dynamics with statistical estimation and hypothesis testing. This way computational models in neuroscience are not only explanat
ory frameworks, but become powerful, quantitative data-analytical tools in themselves that enable researchers to look beyond the data surface and unravel underlying mechanisms. Interactive examples of most methods are provided through a package of MatLAB routines, encouraging a playful approach to the subject, and providing readers with a better feel for the practical aspects of the methods covered.Statistical Inference
Statistical Models
Goals of Model-Based Analysis and Basic Definitions
Principles of Statistical Parameter Estimation
Solving for Parameters in Analytically Intractable Situations
Statistical Hypothesis Testing
Regression Problems
Multiple Linear Regression and the General Linear Model (GLM)
Multivariate Regression and the Multivariate General Linear Model
Canonical Correlation Analysis (CCA)
Ridge and LASSO Regression
Local Linear Regression (LLR)
Basis Expansions and Splines
k-Nearest Neighbors for Regression
Artificial Neural Networks as Nonlinear Regression Tools
Classification Problems
Discriminant Analysis
Fisher’s Discriminant Criterion
Logistic Regression
k-Nearest Neighbors (kNN) for Classification
Maximum Margin Classifiers, Kernels, and Support Vector Machines
Model Complexity and Selection
Penalizing Model Complexity
Estimating Test Error by Cross-Validation
Estimating Test Error by Bootstrapping
Curse of Dimensionality
Variable Selection
Clustering and Density Estimation
Density Estimation
Clustering
Determining the Number of Classes
Mode Hunting
Dimensionality Reduction
Principal Component Analysis (PCA)
Canonical Correlation Analysis (CCA) Revisited
Fisher Discriminant Analysis (FDA) Revisited
Factor Analysis (FA)
Multidimensional Scaling (MDS) and Locally Linear Embedding (LLE)
Independent Component Analysis (ICA)
Linear Time Series Analysis
Basic Descriptive Tools and Terms
Linear Time Series Models
Autoregressive Models for Count and Point Processes
Granger Causality
Linear Time Series Models with Latent Variables
Computational and Neurocognitive Time Series Models
Bootstrapping Time Series
Nonlinear Concepts in Time Series Analysis
Detecting Nonlinearity and Nonparametric Forecasting
Nonparametric Time Series Modeling
Change Point Analysis
Hidden Markov Models
Time Series from a Nonlinear Dynamical Systems Perspective
Discrete-Time Nonlinear Dynamical Systems
Continuous-Time Nonlinear Dynamical Systems
Statistical Inference in Nonlinear Dynamical Systems
Reconstructing State Spaces from Experimental Data
Detecting Causality in Nonlinear Dynamical Systems