Jump to ContentJump to Main Navigation

You are looking at 1-12 of 12 items

  • Keywords: relative entropy x
Clear All Modify Search

View:

Introduction to Large Deviation 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/9780691133157.003.0005
Subject:
Mathematics, Probability / Statistics

This chapter provides an introduction to large deviation theory. It begins with an overview of the motivatio n for the problem under study, focusing on probability distributions and how to construct ... More


Entropy

Robert Alicki and Mark Fannes

in Quantum Dynamical Systems

Published in print:
2001
Published Online:
February 2010
ISBN:
9780198504009
eISBN:
9780191708503
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198504009.003.0009
Subject:
Physics, Theoretical, Computational, and Statistical Physics

This chapter begins with the discussion of various meanings of the entropy: Boltzmann entropy, Shannon entropy, von Neumann entropy. It then presents the basic properties of the von Neumann entropy ... 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


Quantum information I

Vlatko Vedral

in Introduction to Quantum Information Science

Published in print:
2006
Published Online:
January 2010
ISBN:
9780199215706
eISBN:
9780191706783
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199215706.003.0005
Subject:
Physics, Theoretical, Computational, and Statistical Physics

Information is often considered classical in a definite state rather than in a superposition of states. It seems rather strange to consider information in superpositions. Some people would, on the ... More


Measures of entanglement

Vlatko Vedral

in Introduction to Quantum Information Science

Published in print:
2006
Published Online:
January 2010
ISBN:
9780199215706
eISBN:
9780191706783
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199215706.003.0010
Subject:
Physics, Theoretical, Computational, and Statistical Physics

This chapter discusses how entangled two states are. One obvious way is to consider the distillation procedure, in which the entanglement of any state is quantified by how many fully entangled qubits ... More


Quantum information II

Vlatko Vedral

in Introduction to Quantum Information Science

Published in print:
2006
Published Online:
January 2010
ISBN:
9780199215706
eISBN:
9780191706783
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199215706.003.0006
Subject:
Physics, Theoretical, Computational, and Statistical Physics

This chapter discusses the principles of quantum information. The quantum mechanical equivalent of the Shannon noisy-channel communication theorem is obtained, along with some profound statements ... More


The Metrics of Info-Metrics

Amos Golan

in Foundations of Info-Metrics: Modeling, Inference, and Imperfect Information

Published in print:
2017
Published Online:
November 2017
ISBN:
9780199349524
eISBN:
9780199349555
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/oso/9780199349524.003.0003
Subject:
Economics and Finance, Econometrics

In this chapter I present the key ideas and develop the essential quantitative metrics needed for modeling and inference with limited information. I provide the necessary tools to study the ... More


Prior Information

Amos Golan

in Foundations of Info-Metrics: Modeling, Inference, and Imperfect Information

Published in print:
2017
Published Online:
November 2017
ISBN:
9780199349524
eISBN:
9780199349555
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/oso/9780199349524.003.0008
Subject:
Economics and Finance, Econometrics

In this chapter I introduce and quantify prior information and show how to incorporate it into the info-metrics framework. The priors developed arise from fundamental properties of the system, from ... More


Large Deviations Principle for Diffusions

Gopinath Kallianpur and P. Sundar

in Stochastic Analysis and Diffusion Processes

Published in print:
2014
Published Online:
April 2014
ISBN:
9780199657063
eISBN:
9780191781759
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199657063.003.0012
Subject:
Mathematics, Probability / Statistics, Applied Mathematics

Large deviations theory formulated by Varadhan has made a tremendous impact in a variety of fields such as mathematical physics, control theory, and statistics, to name a few. After a brief ... More


Population Dynamics

Daniel Friedman, Barry Sinervo, Daniel Friedman, Barry Sinervo, Daniel Friedman, and Barry Sinervo

in Evolutionary Games in Natural, Social, and Virtual Worlds

Published in print:
2016
Published Online:
August 2016
ISBN:
9780199981151
eISBN:
9780190466657
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199981151.003.0001
Subject:
Economics and Finance, Behavioural Economics

The chapter introduces the concept of fitness, and focuses on the distribution of traits or behaviors within each population. The traits may be biological and governed by genes, or may instead have a ... More


The Blessing and the Curse of the Multiplicative Updates

Daniel Friedman and Barry Sinervo

in Evolutionary Games in Natural, Social, and Virtual Worlds

Published in print:
2016
Published Online:
August 2016
ISBN:
9780199981151
eISBN:
9780190466657
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199981151.003.0010
Subject:
Economics and Finance, Behavioural Economics

This chapter shows how replicator dynamics (in a setting with no frequency dependence) correspond to multiplicative updates studied by computer scientists in the context of online learning. The ... More


Generalized Information Measures and the Analysis of Brain Electrical Signals

A. Plastino and M. T. Martin

in Nonextensive Entropy: Interdisciplinary Applications

Published in print:
2004
Published Online:
November 2020
ISBN:
9780195159769
eISBN:
9780197562024
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/oso/9780195159769.003.0020
Subject:
Earth Sciences and Geography, Atmospheric Sciences

The traditional way of analyzing brain electrical activity, on the basis of electroencephalogram (EEG) records, relies mainly on visual inspection and years of ... More


View: