Advanced Data Analysis in Neuroscience

This book is intended for use in advanced graduate courses in statistics/ machine learning for students from the neuro- and biosciences. At the same time, it offers a valuable guide for all experimental neuroscientists seeking to understand statistical methods at a deeper level, as well as theoretical neuroscientists with a limited background in statistics. It reviews almost all areas of applied statistics, from basic statistical test theory, principles of parameter estimation, linear and nonlinear approaches for regression and classification, and model complexity and selection, to methods for dimensionality reduction and visualization, density estimation and unsupervised clustering. Its focus, however, is linear and nonlinear time series analysis from a dynamical systems perspective. Building on this perspective, the book also aims to convey an understanding of the dynamical mechanisms that could have generated observed neural 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 explanatory frameworks for understanding empirical phenomena, 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. AbarbanelPhysics and Scripps Institution of Oceanography, University of California, San Diego