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Representing Response Times as Random Variables

R. Duncan Luce

in Response Times: Their Role in Inferring Elementary Mental Organization

Published in print:
1991
Published Online:
January 2008
ISBN:
9780195070019
eISBN:
9780199869879
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780195070019.003.0001
Subject:
Psychology, Cognitive Models and Architectures

This chapter begins with a discussion of the study of response times. Response times are treated as observations of a random variable. The mathematics of stochastic processes is then used to ... More


Introduction to Probability and Random Variables

M. Vidyasagar

in Hidden Markov Processes: Theory and Applications to Biology

Published in print:
2014
Published Online:
October 2017
ISBN:
9780691133157
eISBN:
9781400850518
Item type:
chapter
Publisher:
Princeton University Press
DOI:
10.23943/princeton/9780691133157.003.0001
Subject:
Mathematics, Probability / Statistics

This chapter provides an introduction to probability and random variables. Probability theory is an attempt to formalize the notion of uncertainty in the outcome of an experiment. For instance, ... More


Probability and Statistical Distributions

Željko Ivezi, Andrew J. Connolly, Jacob T. VanderPlas, Alexander Gray, Željko Ivezi, Andrew J. Connolly, Jacob T. VanderPlas, and Alexander Gray

in Statistics, Data Mining, and Machine Learning in Astronomy: A Practical Python Guide for the Analysis of Survey Data

Published in print:
2014
Published Online:
October 2017
ISBN:
9780691151687
eISBN:
9781400848911
Item type:
chapter
Publisher:
Princeton University Press
DOI:
10.23943/princeton/9780691151687.003.0003
Subject:
Physics, Particle Physics / Astrophysics / Cosmology

This chapter reviews notation and basic concepts in probability and statistics. The coverage of various topics cannot be complete, and it is aimed at concepts needed to understand material covered in ... More


Introduction to Information Theory

M. Vidyasagar

in Hidden Markov Processes: Theory and Applications to Biology

Published in print:
2014
Published Online:
October 2017
ISBN:
9780691133157
eISBN:
9781400850518
Item type:
chapter
Publisher:
Princeton University Press
DOI:
10.23943/princeton/9780691133157.003.0002
Subject:
Mathematics, Probability / Statistics

This chapter provides an introduction to some elementary aspects of information theory, including entropy in its various forms. Entropy refers to the level of uncertainty associated with a random ... More


 Going, Going …

Ken Binmore

in Playing for Real: Game Theory

Published in print:
2007
Published Online:
May 2007
ISBN:
9780195300574
eISBN:
9780199783748
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780195300574.003.0021
Subject:
Economics and Finance, Microeconomics

The most successful area of game theory is auction design. This chapter offers a short review of the subject. Various traditional auctions are described. After showing that most of these generate the ... More


A review of random variable theory

Daniel T. Gillespie and Effrosyni Seitaridou

in Simple Brownian Diffusion: An Introduction to the Standard Theoretical Models

Published in print:
2012
Published Online:
January 2013
ISBN:
9780199664504
eISBN:
9780191748516
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199664504.003.0002
Subject:
Physics, Soft Matter / Biological Physics

In extending the analysis of diffusion beyond the traditional approach described in Chapter 1, the chapter here finds it necessary to work with random variables. This chapter gives a self-contained, ... More


Classical Probability Theory and Stochastic Processes

Heinz-Peter Breuer and Francesco Petruccione

in The Theory of Open Quantum Systems

Published in print:
2007
Published Online:
January 2010
ISBN:
9780199213900
eISBN:
9780191706349
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199213900.003.01
Subject:
Physics, Theoretical, Computational, and Statistical Physics

This chapter contains a survey of classical probability theory and stochastic processes. It starts with a description of the fundamental concepts of probability space and Kolmogorov axioms. These ... More


Entropy and Mutual Information

Partha P. Mitra and Hemant Bokil

in Observed Brain Dynamics

Published in print:
2007
Published Online:
May 2009
ISBN:
9780195178081
eISBN:
9780199864829
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780195178081.003.0014
Subject:
Neuroscience, Techniques, Molecular and Cellular Systems

In the neuroscience literature, significant use has been made of entropy as a measure of variability, and mutual information as a measure of association. Part of the attraction of these measures ... More


Simulating molecular evolution

ZIHENG YANG

in Computational Molecular Evolution

Published in print:
2006
Published Online:
April 2010
ISBN:
9780198567028
eISBN:
9780191728280
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198567028.003.0009
Subject:
Biology, Evolutionary Biology / Genetics

This chapter discusses basic techniques of computer simulation. Topics covered include random number generator, generation of continuous random variables, generation of discrete random variables, and ... More


PROBABILITY THEORY

Robert M. Mazo

in Brownian Motion: Fluctuations, Dynamics, and Applications

Published in print:
2008
Published Online:
January 2010
ISBN:
9780199556441
eISBN:
9780191705625
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199556441.003.0002
Subject:
Physics, Condensed Matter Physics / Materials

This chapter begins with a review of elementary probability theory, conditional probability, and statistical independence. It explains the notion of a random variable and its distribution function or ... More


 Taking Chances

Ken Binmore

in Playing for Real: Game Theory

Published in print:
2007
Published Online:
May 2007
ISBN:
9780195300574
eISBN:
9780199783748
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780195300574.003.0003
Subject:
Economics and Finance, Microeconomics

This chapter shows how risk can be introduced into the rules of a game by admitting chance moves. The Monty Hall problem is offered as an example. Elementary probability theory is reviewed, and ... More


Stochastic Processes and Stochastic Calculus

Claus Munk

in Fixed Income Modelling

Published in print:
2011
Published Online:
September 2011
ISBN:
9780199575084
eISBN:
9780191728648
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199575084.003.0003
Subject:
Economics and Finance, Financial Economics

The price of an asset at a future point in time will typically be unknown, i.e. a random variable. In order to describe the uncertain evolution in the price of the asset over time, we need a ... More


Real-valued Random Processes

Arno Berger and Theodore P. Hill

in An Introduction to Benford's Law

Published in print:
2015
Published Online:
October 2017
ISBN:
9780691163062
eISBN:
9781400866588
Item type:
chapter
Publisher:
Princeton University Press
DOI:
10.23943/princeton/9780691163062.003.0008
Subject:
Mathematics, Probability / Statistics

Benford's law arises naturally in a variety of stochastic settings, including products of independent random variables, mixtures of random samples from different distributions, and iterations of ... More


Properties of random variables

M. D. Edge

in Statistical Thinking from Scratch: A Primer for Scientists

Published in print:
2019
Published Online:
October 2019
ISBN:
9780198827627
eISBN:
9780191866463
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/oso/9780198827627.003.0006
Subject:
Biology, Biomathematics / Statistics and Data Analysis / Complexity Studies

In this chapter, the behavior of random variables is summarized using the concepts of expectation, variance, and covariance. The expectation is a measurement of the location of a random variable’s ... More


Random Variables

James Davidson

in Stochastic Limit Theory: An Introduction for Econometricians

Published in print:
1994
Published Online:
November 2003
ISBN:
9780198774037
eISBN:
9780191596117
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/0198774036.003.0008
Subject:
Economics and Finance, Econometrics

Specializing the concepts of Ch. 7 to the case of real variables, this chapter introduces distribution functions, discrete and continuous distributions, and describes examples such as the binomial, ... More


Degree of Belief is Expected Truth Value

Nicholas J. J. Smith

in Cuts and Clouds: Vagueness, its Nature, & its Logic

Published in print:
2010
Published Online:
May 2010
ISBN:
9780199570386
eISBN:
9780191722134
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199570386.003.0029
Subject:
Philosophy, Logic/Philosophy of Mathematics, Metaphysics/Epistemology

A number of authors have noted that vagueness engenders degrees of belief, but that these degrees of belief do not behave like subjective probabilities. So should we countenance two different kinds ... More


Probability and random variables

M. D. Edge

in Statistical Thinking from Scratch: A Primer for Scientists

Published in print:
2019
Published Online:
October 2019
ISBN:
9780198827627
eISBN:
9780191866463
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/oso/9780198827627.003.0005
Subject:
Biology, Biomathematics / Statistics and Data Analysis / Complexity Studies

This chapter considers the rules of probability. Probabilities are non-negative, they sum to one, and the probability that either of two mutually exclusive events occurs is the sum of the probability ... More


Langevin treatment of the Fokker–Planck process

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/9780198567769.003.0010
Subject:
Physics, Theoretical, Computational, and Statistical Physics

This chapter discusses the Langevin treatment of the Fokker–Planck process and diffusion. The form of Langevin equation used is different from the stochastic differential equation using Ito's ... More


Into the Unknown: Modeling Uncertainty

Michael R. Powers

in Acts of God and Man: Ruminations on Risk and Insurance

Published in print:
2014
Published Online:
November 2015
ISBN:
9780231153676
eISBN:
9780231527057
Item type:
chapter
Publisher:
Columbia University Press
DOI:
10.7312/columbia/9780231153676.003.0002
Subject:
Economics and Finance, Development, Growth, and Environmental

Every manifestation of risk is associated with one or more unknown quantities. For instance, in the case of the inevitable death of an individual, it is primarily the time of death that is unknown. ... More


Spectral measurement and correlation

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/9780198567769.003.0004
Subject:
Physics, Theoretical, Computational, and Statistical Physics

This chapter compares three definitions of noise. The first is the standard engineering definition that takes a Fourier transform over a finite time interval, squares it, divides by the time, and ... More


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