Likelihood Methods for Neural Spike Train Data Analysis - Computational Neuroscience: A Comprehensive Approach - page 250

Chapter 9

LikelihoodMethodsforNeural
SpikeTrainDataAnalysis

Emery N. Brown, Riccardo Barbieri, Uri T. Eden, and Loren M. Frank
Neuroscience Statistics Research Laboratory, Department of Anesthesia and
Critical Care, Massachusetts General Hospital, U.S., Division of Health Sciences
and Technology, Harvard Medical School, Massachusetts Institute of Technology,
U.S.

CONTENTS
9.1 Introduction
9.2 Theory
9.2.1 The conditional intensity function and interspike interval proba-
bility density
9.2.2 The likelihood function of a point process model
9.2.3 Summarizing the likelihood function: maximum likelihood esti-
mationandFisherinformation
9.2.4 Properties of maximum likelihood estimates
9.2.5 Model selection and model goodness-of-fit
9.3 Applications
9.3.1 Ananalysisofthespikingactivityofaretinalneuron
9.3.2 An analysis of hippocampal place-specific firing activity
9.3.3 An analysis of the spatial receptive field dynamics of a hip-
pocampalneuron
9.4 Conclusion
9.5 Appendix
References

9.1 Introduction

Computational neuroscience uses mathematical models to study how neural systems
represent and transmit information. Although modeling in computational neuro-
science spans a range of mathematical approaches, the discipline may be divided
approximately into two schools. The first school uses detailed biophysical (Hodgkin
and Huxley and their variants) models of individual neurons, networks of neurons
or artificial neural network models to study emergent behaviors of neural systems.