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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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