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E-raamat: Advanced Data Analysis in Neuroscience: Integrating Statistical and Computational Models

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Advanced Data Analysis in Neuroscience: Integrating Statistical and Computational ModelsSuurem pilt
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This 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.

"Computational neuroscience is essential for integrating and providing a basis for understanding the myriads of remarkable laboratory data on nervous system functions. Daniel Durstewitz has excellently covered the breadth of computational neuroscience from statistical interpretations of data to biophysically based modeling of the neurobiological sources of those data. His presentation is clear, pedagogically sound, and readily useable by experts and beginners alike. It is a pleasure to recommend this very well crafted discussion to experimental neuroscientists as well

as mathematically well versed Physicists. The book acts as a window to the issues, to the questions, and to the tools for finding the answers to interesting inquiries about brains and how they function."

Henry D. I. Abarbanel

Physics and Scripps Institution of Oceanography, University of California, San Diego

“This book delivers a clear and thorough introduction to sophisticated analysis approaches useful in computational neuroscience. The models described and the examples provided will help readers develop critical intuitions into what the methods reveal about data. The overall approach of the book reflects the extensive experience Prof. Durstewitz has developed as a leading practitioner of computational neuroscience. “

Bruno B. Averbeck

1 Statistical Inference
1(32)
1.1 Statistical Models
2(5)
1.2 Goals of Model-Based Analysis and Basic Definitions
7(3)
1.3 Principles of Statistical Parameter Estimation
10(5)
1.3.1 Least-Squared Error (LSE) Estimation
10(1)
1.3.2 Maximum Likelihood (ML) Estimation
11(2)
1.3.3 Bayesian Inference
13(2)
1.4 Solving for Parameters in Analytically Intractable Situations
15(4)
1.4.1 Gradient Descent and Newton-Raphson
15(2)
1.4.2 Expectation-Maximization (EM) Algorithm
17(1)
1.4.3 Optimization in Rough Territory
18(1)
1.5 Statistical Hypothesis Testing
19(14)
1.5.1 Exact Tests
19(2)
1.5.2 Asymptotic Tests
21(5)
1.5.3 Bootstrap (BS) Methods
26(4)
1.5.4 Multiple Testing Problem
30(3)
2 Regression Problems
33(24)
2.1 Multiple Linear Regression and the General Linear Model (GLM)
34(5)
2.2 Multivariate Regression and the Multivariate General Linear Model
39(4)
2.3 Canonical Correlation Analysis (CCA)
43(2)
2.4 Ridge and LASSO Regression
45(3)
2.5 Local Linear Regression (LLR)
48(2)
2.6 Basis Expansions and Splines
50(2)
2.7 k-Nearest Neighbors for Regression
52(1)
2.8 Artificial Neural Networks as Nonlinear Regression Tools
53(4)
3 Classification Problems
57(16)
3.1 Discriminant Analysis
58(4)
3.2 Fisher's Discriminant Criterion
62(2)
3.3 Logistic Regression
64(2)
3.4 k-Nearest Neighbors (kNN) for Classification
66(1)
3.5 Maximum Margin Classifiers, Kernels, and Support Vector Machines
67(6)
3.5.1 Maximum Margin Classifiers (MMC)
67(2)
3.5.2 Kernel Functions
69(2)
3.5.3 Support Vector Machines (SVM)
71(2)
4 Model Complexity and Selection
73(12)
4.1 Penalizing Model Complexity
75(1)
4.2 Estimating Test Error by Cross-Validation
76(2)
4.3 Estimating Test Error by Bootstrapping
78(1)
4.4 Curse of Dimensionality
79(2)
4.5 Variable Selection
81(4)
5 Clustering and Density Estimation
85(20)
5.1 Density Estimation
86(7)
5.1.1 Gaussian Mixture Models (GMMs)
86(3)
5.1.2 Kernel Density Estimation (KDE)
89(4)
5.2 Clustering
93(5)
5.2.1 k-Means and k-Medoids
94(1)
5.2.2 Hierarchical Cluster Analysis
95(3)
5.3 Determining the Number of Classes
98(3)
5.4 Mode Hunting
101(4)
6 Dimensionality Reduction
105(16)
6.1 Principal Component Analysis (PCA)
105(4)
6.2 Canonical Correlation Analysis (CCA) Revisited
109(1)
6.3 Fisher Discriminant Analysis (FDA) Revisited
109(1)
6.4 Factor Analysis (FA)
109(4)
6.5 Multidimensional Scaling (MDS) and Locally Linear Embedding (LLE)
113(4)
6.6 Independent Component Analysis (ICA)
117(4)
7 Linear Time Series Analysis
121(62)
7.1 Basic Descriptive Tools and Terms
122(10)
7.1.1 Autocorrelation
122(2)
7.1.2 Power Spectrum
124(2)
7.1.3 White Noise
126(1)
7.1.4 Stationarity and Ergodicity
127(3)
7.1.5 Multivariate Time Series
130(2)
7.2 Linear Time Series Models
132(9)
7.2.1 Estimation of Parameters in AR Models
136(3)
7.2.2 Statistical Inference on Model Parameters
139(2)
7.3 Autoregressive Models for Count and Point Processes
141(4)
7.4 Granger Causality
145(5)
7.5 Linear Time Series Models with Latent Variables
150(21)
7.5.1 Linear State Space Models
152(12)
7.5.2 Gaussian Process Factor Analysis
164(1)
7.5.3 Latent Variable Models for Count and Point Processes
165(6)
7.6 Computational and Neurocognitive Time Series Models
171(5)
7.7 Bootstrapping Time Series
176(7)
8 Nonlinear Concepts in Time Series Analysis
183(16)
8.1 Detecting Nonlinearity and Nonparametric Forecasting
184(3)
8.2 Nonparametric Time Series Modeling
187(1)
8.3 Change Point Analysis
188(5)
8.4 Hidden Markov Models
193(6)
9 Time Series from a Nonlinear Dynamical Systems Perspective
199(66)
9.1 Discrete-Time Nonlinear Dynamical Systems
199(14)
9.1.1 Univariate Maps and Basic Concepts
200(7)
9.1.2 Multivariate Maps and Recurrent Neural Networks
207(6)
9.2 Continuous-Time Nonlinear Dynamical Systems
213(23)
9.2.1 Review of Basic Concepts and Phenomena in Nonlinear Systems Described by Differential Equations
215(15)
9.2.2 Nonlinear Oscillations and Phase-Locking
230(6)
9.3 Statistical Inference in Nonlinear Dynamical Systems
236(20)
9.3.1 Nonlinear Dynamical Model Estimation in Discrete and Continuous Time
237(13)
9.3.2 Dynamic Causal Modeling
250(2)
9.3.3 Special Issues in Nonlinear (Chaotic) Latent Variable Models
252(4)
9.4 Reconstructing State Spaces from Experimental Data
256(5)
9.5 Detecting Causality in Nonlinear Dynamical Systems
261(4)
References 265(20)
Index 285
Daniel Durstewitz is Professor for Theoretical Neuroscience and Head of the Department of Theoretical Neuroscience at the Central Institute of Mental Health, Mannheim, and the University of Heidelberg. He is also the coordinator and a director of the Bernstein Center for Computational Neuroscience Heidelberg-Mannheim. He has authored numerous articles in the fields of theoretical and computational neuroscience, applying and advancing various statistical and modeling techniques. Together with Jeremy Seamans, he has also developed an influential computational theory of dopamine function in the prefrontal cortex.
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