## OBJECTIVE BAYESIANISM

*Jon Williamson*

### in Bayesian Nets and Causality: Philosophical and Computational Foundations

- Published in print:
- 2004
- Published Online:
- September 2007
- ISBN:
- 9780198530794
- eISBN:
- 9780191712982
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780198530794.003.0005
- Subject:
- Mathematics, Logic / Computer Science / Mathematical Philosophy

Objective Bayesianism imposes two norms on degrees of belief: degrees of belief should be constrained by empirical information and they should otherwise be as equivocal as possible. The origins of ... More

## An introduction to maximum entropy

*Peter Main*

### in Crystal Structure Analysis: Principles and Practice

- Published in print:
- 2009
- Published Online:
- September 2009
- ISBN:
- 9780199219469
- eISBN:
- 9780191722516
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199219469.003.0011
- Subject:
- Physics, Crystallography

Maximum entropy methods are used in crystallography for estimating reflection phases among other applications. This chapter explains the basic concepts behind maximum entropy, including entropy ... More

## Quantum Transport in Mesoscopic Systems: Complexity and Statistical Fluctuations. A Maximum Entropy Viewpoint

*Pier A. Mello and Narendra Kumar*

- Published in print:
- 2004
- Published Online:
- September 2007
- ISBN:
- 9780198525820
- eISBN:
- 9780191712234
- Item type:
- book

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780198525820.001.0001
- Subject:
- Physics, Condensed Matter Physics / Materials

This book presents a statistical theory of complex wave scattering and quantum transport in a class of physical systems of current interest having chaotic classical dynamics (e.g., microwave cavities ... More

## INTRODUCTION

*Jon Williamson*

### in Bayesian Nets and Causality: Philosophical and Computational Foundations

- Published in print:
- 2004
- Published Online:
- September 2007
- ISBN:
- 9780198530794
- eISBN:
- 9780191712982
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780198530794.003.0001
- Subject:
- Mathematics, Logic / Computer Science / Mathematical Philosophy

This chapter describes the central claims of the book. From a philosophical point of view, the book argues for an objective Bayesian interpretation of probability and an epistemic interpretation of ... More

## THE MAXIMUM-ENTROPY APPROACH: AN INFORMATION-THEORETIC VIEWPOINT

*Pier A. Mello and Narendra Kumar*

### in Quantum Transport in Mesoscopic Systems: Complexity and Statistical Fluctuations. A Maximum Entropy Viewpoint

- Published in print:
- 2004
- Published Online:
- September 2007
- ISBN:
- 9780198525820
- eISBN:
- 9780191712234
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780198525820.003.0005
- Subject:
- Physics, Condensed Matter Physics / Materials

This chapter motivates and discusses the basic idea of information-theoretic entropy, i.e., the Shannon entropy, and the maximum-entropy approach (MEA) based on it. The concepts of the prior and of ... More

## Statistical Mechanics and Information Theory for Complex Systems

*Stefan Thurner, Rudolf Hanel, and Peter Klimekl*

### in Introduction to the Theory of Complex Systems

- Published in print:
- 2018
- Published Online:
- November 2018
- ISBN:
- 9780198821939
- eISBN:
- 9780191861062
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/oso/9780198821939.003.0006
- Subject:
- Physics, Theoretical, Computational, and Statistical Physics

Most complex systems are statistical systems. Statsitical mechanics and information theory usually do not apply to complex systems because the latter break the assumptions of ergodicity, ... More

## LANGUAGE CHANGE

*Jon Williamson*

### in Bayesian Nets and Causality: Philosophical and Computational Foundations

- Published in print:
- 2004
- Published Online:
- September 2007
- ISBN:
- 9780198530794
- eISBN:
- 9780191712982
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780198530794.003.0012
- Subject:
- Mathematics, Logic / Computer Science / Mathematical Philosophy

This chapter discusses the situation in which an agent's language or domain may change. It is argued — against a principle of language invariance — that language contains implicit knowledge and so ... More

## Incommensurate Crystallography

*Sander van Smaalen*

- Published in print:
- 2007
- Published Online:
- January 2008
- ISBN:
- 9780198570820
- eISBN:
- 9780191718762
- Item type:
- book

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780198570820.001.0001
- Subject:
- Physics, Crystallography

Aperiodic crystals are crystalline materials with atomic structures that lack translational symmetry. This book gives a comprehensive account of the superspace theory for the description of the ... More

## Energy flow

*David M. Wilkinson*

### in Fundamental Processes in Ecology: An earth systems approach

- Published in print:
- 2006
- Published Online:
- September 2007
- ISBN:
- 9780198568469
- eISBN:
- 9780191717611
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780198568469.003.0002
- Subject:
- Biology, Ecology

The second law of thermodynamics is central to understanding ecology, although it is ignored by most ecology text books. It follows from the second law that all organisms must draw free energy from ... More

## Why making Bayesian networks objectively Bayesian makes sense

*Dawn E. Holmes*

### in Causality in the Sciences

- Published in print:
- 2011
- Published Online:
- September 2011
- ISBN:
- 9780199574131
- eISBN:
- 9780191728921
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199574131.003.0028
- Subject:
- Mathematics, Logic / Computer Science / Mathematical Philosophy

It is well‐known that Bayesian networks are so‐called because of their use of Bayes theorem for probabilistic inference. However, since Bayesian networks commonly use frequentist probabilities ... More

## Updating

*Jon Williamson*

### in In Defence of Objective Bayesianism

- Published in print:
- 2010
- Published Online:
- September 2010
- ISBN:
- 9780199228003
- eISBN:
- 9780191711060
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199228003.003.0004
- Subject:
- Mathematics, Probability / Statistics, Logic / Computer Science / Mathematical Philosophy

The goal of this chapter is to respond to a criticism of objective Bayesianism that concerns the updating of degrees of belief. Objective Bayesianism has often been dismissed on account of ... More

## ELECTRON DENSITY IN SUPERSPACE

*Sander Van Smaalen*

### in Incommensurate Crystallography

- Published in print:
- 2007
- Published Online:
- January 2008
- ISBN:
- 9780198570820
- eISBN:
- 9780191718762
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780198570820.003.0008
- Subject:
- Physics, Crystallography

This chapter considers the properties of the generalized electron density as it can be displayed in superspace. Fourier maps and difference Fourier maps allow the visual inspection of various ... 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

## Entropy Maximization

*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/9780199349524.003.0004
- Subject:
- Economics and Finance, Econometrics

In this chapter I develop the essential maximum entropy procedure, which is an inversion procedure for inferring an unknown probability distribution function from incomplete information. The ... More

## The Probability Connection

*T. Grandy Walter*

### in Entropy and the Time Evolution of Macroscopic Systems

- Published in print:
- 2008
- Published Online:
- September 2008
- ISBN:
- 9780199546176
- eISBN:
- 9780191720161
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199546176.003.0003
- Subject:
- Physics, Theoretical, Computational, and Statistical Physics

This chapter presents a brief introduction to probability as logic. The principle of maximum entropy is then developed as an algorithm of probability theory for the construction of prior ... More

## Maximum Entropy and Ecology: A Theory of Abundance, Distribution, and Energetics

*John Harte*

- Published in print:
- 2011
- Published Online:
- December 2013
- ISBN:
- 9780199593415
- eISBN:
- 9780191774614
- Item type:
- book

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199593415.001.0001
- Subject:
- Biology, Ecology

A goal of every science is comprehensive theory that is predictive, realistic, and parsimonious. Is such theory possible in ecology? The sheer complexity, historical contingency, and scale-dependence ... More

## Patterson methods in powder diffraction: maximum entropy and symmetry minimum function techniques

*Michael A. Estermann and William I. F. David*

### in Structure Determination from Powder Diffraction Data

- Published in print:
- 2006
- Published Online:
- January 2010
- ISBN:
- 9780199205530
- eISBN:
- 9780191718076
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199205530.003.0012
- Subject:
- Physics, Condensed Matter Physics / Materials

Starting from a definition of the relationship between a crystal structure and its Patterson function, this chapter considers the role of the Patterson function in the particular context of powder ... More

## Constructing the State

*Jochen Rau*

### in Statistical Physics and Thermodynamics: An Introduction to Key Concepts

- Published in print:
- 2017
- Published Online:
- November 2017
- ISBN:
- 9780199595068
- eISBN:
- 9780191844300
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/oso/9780199595068.003.0003
- Subject:
- Physics, Theoretical, Computational, and Statistical Physics

The limited data available about a macroscopic system may come in various forms: sharp constraints, expectation values, or control parameters. While these data impose constraints on the state, they ... 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

## A maximum entropy approach to structure solution

*Christopher J. Gilmore, Kenneth Shankland, and Wei Dong*

### in Structure Determination from Powder Diffraction Data

- Published in print:
- 2006
- Published Online:
- January 2010
- ISBN:
- 9780199205530
- eISBN:
- 9780191718076
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199205530.003.0014
- Subject:
- Physics, Condensed Matter Physics / Materials

This chapter describes a combined maximum entropy/log-likelihood gain approach to crystal structure determination from powder diffraction data. The approach is described step-by-step, with a ... More