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## INTRODUCTION

*Mathew Penrose*

### in Random Geometric Graphs

- Published in print:
- 2003
- Published Online:
- September 2007
- ISBN:
- 9780198506263
- eISBN:
- 9780191707858
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780198506263.003.0001
- Subject:
- Mathematics, Probability / Statistics

This introductory chapter contains a general discussion of both the historical and the applied background behind the study of random geometric graphs. A brief overview is presented, along with some ... More

## Random graphs with general degree distributions: This chapter describes more sophisticated random graph models that mimic networks with arbitrary degree distributions

*M. E. J. Newman*

### in Networks: An Introduction

- Published in print:
- 2010
- Published Online:
- September 2010
- ISBN:
- 9780199206650
- eISBN:
- 9780191594175
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199206650.003.0013
- Subject:
- Physics, Theoretical, Computational, and Statistical Physics

The previous chapter looked at the classic random graph model, in which pairs of vertices are connected at random with uniform probabilities. Although this model has proved tremendously useful as a ... More

## Modelling Multivariate Counts Varying Continuously in Space *

*Alexandra M. Schmidt and Marco A. Rodríguez*

### in Bayesian Statistics 9

- Published in print:
- 2011
- Published Online:
- January 2012
- ISBN:
- 9780199694587
- eISBN:
- 9780191731921
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199694587.003.0020
- Subject:
- Mathematics, Probability / Statistics

We discuss models for multivariate counts observed at fixed spatial locations of a region of interest. Our approach is based on a continuous mixture of independent Poisson distributions. The mixing ... More

## Statistical Power and Sample Size Calculations

*Steve Selvin*

### in Statistical Analysis of Epidemiologic Data

- Published in print:
- 2004
- Published Online:
- September 2009
- ISBN:
- 9780195172805
- eISBN:
- 9780199865697
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780195172805.003.03
- Subject:
- Public Health and Epidemiology, Public Health, Epidemiology

This chapter discusses the power of a statistical test and the closely related issue of sample size. Topics covered include normal distribution, Poisson distribution, sample size, and loss of ... More

## Classical random graphs

*Sergey N. Dorogovtsev*

### in Lectures on Complex Networks

- Published in print:
- 2010
- Published Online:
- May 2010
- ISBN:
- 9780199548927
- eISBN:
- 9780191720574
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199548927.003.0002
- Subject:
- Physics, Theoretical, Computational, and Statistical Physics

This chapter gives insight into the simplest and most studied random networks: the classical random graphs. The Erdös–Rényi and Gilbert models are described, and some of their properties and ... More

## WHAT ARE NETWORKS?

*S. N. Dorogovtsev and J. F. F. Mendes*

### in Evolution of Networks: From Biological Nets to the Internet and WWW

- Published in print:
- 2003
- Published Online:
- January 2010
- ISBN:
- 9780198515906
- eISBN:
- 9780191705670
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780198515906.003.0002
- Subject:
- Physics, Soft Matter / Biological Physics

This chapter introduces the basic characteristics and notions of graph theory and the science of networks: degree, degree distribution, clustering coefficient, the average length of the shortest path ... More

## Randomness

*Peter Coles*

### in From Cosmos to Chaos: The Science of Unpredictability

- Published in print:
- 2006
- Published Online:
- January 2010
- ISBN:
- 9780198567622
- eISBN:
- 9780191718250
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780198567622.003.0005
- Subject:
- Physics, Theoretical, Computational, and Statistical Physics

This chapter examines randomness and how it applies (or does not) in both abstract mathematics and in physical systems. There are many different ways in which a sequence of events could be said to be ... More

## Rare Events

*Steven J. Osterlind*

### in The Error of Truth: How History and Mathematics Came Together to Form Our Character and Shape Our Worldview

- Published in print:
- 2019
- Published Online:
- January 2019
- ISBN:
- 9780198831600
- eISBN:
- 9780191869532
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/oso/9780198831600.003.0011
- Subject:
- Mathematics, Logic / Computer Science / Mathematical Philosophy

This chapter shows that the quantification worldview was not spreading uniformly across even the developed world. In the United States, the spread was slow, because nearly everyone was consumed with ... More

## Random walk of light in turbid media

*Melvin Lax, Wei Cai, and Min Xu*

### in Random Processes in Physics and Finance

- Published in print:
- 2006
- Published Online:
- January 2010
- ISBN:
- 9780198567769
- eISBN:
- 9780191718359
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780198567769.003.0013
- Subject:
- Physics, Theoretical, Computational, and Statistical Physics

The random motion of particles in a turbid medium, due to multiple elastic scattering, obeys the classic Boltzmann transport equation. This chapter shows how the center position and the diffusion ... More

## Generalized Linear Models for Data with Non-Normal Distributions

*Andy Hector*

### in The New Statistics with R: An Introduction for Biologists

- Published in print:
- 2015
- Published Online:
- March 2015
- ISBN:
- 9780198729051
- eISBN:
- 9780191795855
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780198729051.003.0009
- Subject:
- Biology, Biomathematics / Statistics and Data Analysis / Complexity Studies, Ecology

This chapter looks at three of the main types of generalized linear model (GLM). GLMs using the Poisson distribution are a good starting place when dealing with integer count data. The default log ... More

## Non-Gaussian and nonlinear illustrations

*J. Durbin and S.J. Koopman*

### in Time Series Analysis by State Space Methods: Second Edition

- Published in print:
- 2012
- Published Online:
- December 2013
- ISBN:
- 9780199641178
- eISBN:
- 9780191774881
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199641178.003.0014
- Subject:
- Mathematics, Probability / Statistics

This chapter discusses examples which illustrate the methods that were developed in Part II for analysing observations using non-Gaussian and nonlinear state space models. These include the monthly ... More

## Advanced Topics

*Carey Witkov and Keith Zengel*

### in Chi-Squared Data Analysis and Model Testing for Beginners

- Published in print:
- 2019
- Published Online:
- November 2019
- ISBN:
- 9780198847144
- eISBN:
- 9780191882074
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/oso/9780198847144.003.0007
- Subject:
- Physics, Theoretical, Computational, and Statistical Physics, Particle Physics / Astrophysics / Cosmology

A variety of advanced topics are introduced to offer greater challenge for beginners and to answer thorny questions often asked by early researchers who are just starting to use chi-squared analysis. ... More

## Laser oscillation and pumping mechanisms

*Warren Nagourney*

### in Quantum Electronics for Atomic Physics and Telecommunication: Second Edition

- Published in print:
- 2014
- Published Online:
- June 2014
- ISBN:
- 9780199665488
- eISBN:
- 9780191779442
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199665488.003.0006
- Subject:
- Physics, Atomic, Laser, and Optical Physics

This chapter combines the results of Chapters 3 and 5 by placing an amplifying medium in a resonant cavity and evaluating the behavior of the resulting laser oscillator. First, the conditions for ... More

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