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Stochastic Methods in Neuroscience

Carlo Laing and Gabriel J Lord (eds)

Published in print:
2009
Published Online:
February 2010
ISBN:
9780199235070
eISBN:
9780191715778
Item type:
book
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199235070.001.0001
Subject:
Mathematics, Biostatistics

We give a brief introduction to modelling in mathematical neuroscience, to stochastic processes, and stochastic differential equations as well as an overview of the book.


A Brief Introduction to Some Simple Stochastic Processes

Benjamin Lindner

in Stochastic Methods in Neuroscience

Published in print:
2009
Published Online:
February 2010
ISBN:
9780199235070
eISBN:
9780191715778
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199235070.003.0001
Subject:
Mathematics, Biostatistics

This chapter gives an overview of simple continuous, two-state, and point processes playing a role in theoretical neuroscience. First, various characteristics of these stochastic processes are ... More


Neural Coherence and Stochastic Resonance

André Longtin

in Stochastic Methods in Neuroscience

Published in print:
2009
Published Online:
February 2010
ISBN:
9780199235070
eISBN:
9780191715778
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199235070.003.0004
Subject:
Mathematics, Biostatistics

This chapter concerns the influence of noise and periodic rhythms on the firing patterns of neurons in their subthreshold regime. Such a regime conceals many computations that lead to successive ... More


Population Density Methods in Large-Scale Neural Network Modelling

Daniel Tranchina

in Stochastic Methods in Neuroscience

Published in print:
2009
Published Online:
February 2010
ISBN:
9780199235070
eISBN:
9780191715778
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199235070.003.0007
Subject:
Mathematics, Biostatistics

Population density methods have a rich history in theoretical and computational neuroscience. In earlier years, these methods were used in large part to study the statistics of spike trains. Starting ... More


Statistical Models of Spike Trains

Liam Paninski, Emery N. Brown, Satish Iyengar, and Robert E. Kass

in Stochastic Methods in Neuroscience

Published in print:
2009
Published Online:
February 2010
ISBN:
9780199235070
eISBN:
9780191715778
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199235070.003.0010
Subject:
Mathematics, Biostatistics

Spiking neurons make inviting targets for analytical methods based on stochastic processes: spike trains carry information in their temporal patterning, yet they are often highly irregular across ... More


Generalized Linear Mixed Models

Ludwig Fahrmeir and Thomas Kneib

in Bayesian Smoothing and Regression for Longitudinal, Spatial and Event History Data

Published in print:
2011
Published Online:
September 2011
ISBN:
9780199533022
eISBN:
9780191728501
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199533022.003.0003
Subject:
Mathematics, Probability / Statistics, Biostatistics

This chapter gives an introduction to linear and generalized linear mixed models. The primary goal is to describe concepts for statistical modelling and inference in this class of models that are ... More


Semiparametric Mixed Models for Longitudinal Data

Ludwig Fahrmeir and Thomas Kneib

in Bayesian Smoothing and Regression for Longitudinal, Spatial and Event History Data

Published in print:
2011
Published Online:
September 2011
ISBN:
9780199533022
eISBN:
9780191728501
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199533022.003.0004
Subject:
Mathematics, Probability / Statistics, Biostatistics

This chapter considers Bayesian inference in semiparametric mixed models (SPMMs) for longitudinal data. Section 4.1 assumes Gaussian smoothness priors, focusing on Bayesian P-splines in combination ... More


Spatial Smoothing, Interactions and Geoadditive Regression

Ludwig Fahrmeir and Thomas Kneib

in Bayesian Smoothing and Regression for Longitudinal, Spatial and Event History Data

Published in print:
2011
Published Online:
September 2011
ISBN:
9780199533022
eISBN:
9780191728501
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199533022.003.0005
Subject:
Mathematics, Probability / Statistics, Biostatistics

This chapter provides an introduction to Bayesian spatial smoothing as a subject of interest in its own right, it points out the close relation between modelling interactions and spatial effects, and ... More


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