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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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