Statistical Techniques for Neuroscientists

Young K. Truong, Mechelle M. Lewis

• Publisher: CRC Press
• Year: 2016
• Print ISBN: 9781466566149
• eBook ISBN: 9781315356754
• Edition: 1
• Topic: Matemáticas
• Subtopic: Probabilidad y estadística

Statistical Techniques for Neuroscientists introduces new and useful methods for data analysis involving simultaneous recording of neuron or large cluster (brain region) neuron activity. The statistical estimation and tests of hypotheses are based on the likelihood principle derived from stationary point processes and time series. Algorithms and software development are given in each chapter to reproduce the computer simulated results described therein.

The book examines current statistical methods for solving emerging problems in neuroscience. These methods have been applied to data involving multichannel neural spike train, spike sorting, blind source separation, functional and effective neural connectivity, spatiotemporal modeling, and multimodal neuroimaging techniques. The author provides an overview of various methods being applied to specific research areas of neuroscience, emphasizing statistical principles and their software. The book includes examples and experimental data so that readers can understand the principles and master the methods.

The first part of the book deals with the traditional multivariate time series analysis applied to the context of multichannel spike trains and fMRI using respectively the probability structures or likelihood associated with time-to-fire and discrete Fourier transforms (DFT) of point processes. The second part introduces a relatively new form of statistical spatiotemporal modeling for fMRI and EEG data analysis. In addition to neural scientists and statisticians, anyone wishing to employ intense computing methods to extract important features and information directly from data rather than relying heavily on models built on leading cases such as linear regression or Gaussian processes will find this book extremely helpful.

Part I

Statistical Analysis of Neural Spike Train Data

1 Statistical Modeling of Neural Spike Train Data

Ruiwen Zhang

SAS Institute

Shih-Chieh Lin

NIH

Haipeng Shen

University of Hong Kong, China

Young K. Truong

University of North Carolina at Chapel Hill

CONTENTS

1.1 Introduction

1.2 Point Process and Conditional Intensity Function

1.3 The Likelihood Function of a Point Process Model

1.4 Continuous State-Space Model

1.4.1 Kernel Smoothing

1.4.2 Adaptive Kernel Smoothing

1.4.3 Kernel Bandwidth Optimization

1.4.4 Smoothing Splines

1.4.5 Real Data Analysis

1.5 M-Files for Simulation

1.6 M-Files for Real Data

1.7 R Files for Real Data

Bibliography

The advance of the multi-electrode has made the field of neural science feasible to record spike trains simultaneously from an ensemble of neurons. However, the statistical techniques for analyzing large-scale simultaneously recorded spike train data have not developed as satisfactorily as the experimental techniques for obtaining these data. This chapter describes a very flexible statistical procedure for modeling an ensemble of neural spike trains, followed with the associated estimation method for making an inference for the functional connectivity based on the statistical results. To approach this problem in a more concrete manner, we use stochastic point processes to develop a statistical model for analyzing an ensemble of spiking activities from noncholinergic basal forebrain neurons [11]. The formulation is equipped with the likelihood (or loosely, the probability) of the occurrence of the neural spike train data, based on which the statistical estimation and inference will be carried out. The model can assess the association or correlation between a target neuron and its peers.

1.1 INTRODUCTION

It is known that neurons, even when they are apart in the brain, often exhibit correlated firing patterns [22]. For instance, coordinated interaction among cortical neurons is known to play an indispensable role in mediating many complex brain functions with highly intricate network structures [23]. A procedure to examine the underlying connectivity between neurons can be stated in the following way. For a target neuron i in a population of N observed neurons, we need to identify a subset of neurons that affect the firing of the target in some statistical sense.

In the study of neural plasticity and network structure, it is desirable to infer the underlying functional connectivity between the recorded neurons. In the analysis of neural spike trains, functional connectivity is defined in terms of the statistical dependence observed between the spike trains from distributed and often spatially remote neuronal units [6]. This can result from the presence of a synaptic link between neurons, or it can be observed when two unlinked neurons respond to a common driving input.

Characterization of the functional network requires simultaneous monitoring of neural constituents while subjects carry out certain fu...

Table of contents

• Cover
• Half Title
• Title Page
• Copyright Page
• Dedication
• Table of Contents
• Preface
• Editors
• Contributors
• List of Figures
• List of Tables
• PART I Statistical Analysis of Neural Spike Train Data
• PART II Statistical Analysis of fMRI Data
• Index