## Applications of Stochastic Geometry in Image Analysis

*Marie‐Colette N.M. van Lieshout*

### in New Perspectives in Stochastic Geometry

- Published in print:
- 2009
- Published Online:
- February 2010
- ISBN:
- 9780199232574
- eISBN:
- 9780191716393
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199232574.003.0013
- Subject:
- Mathematics, Geometry / Topology

A discussion is given of various stochastic geometry models (random fields, sequential object processes, polygonal field models) which can be used in intermediate‐ and high‐level image analysis. Two ... More

## Statistical Inference in MEG Distributed Source Imaging

*Dimitrios Pantazis and Richard M. Leahy*

### in MEG: An Introduction to Methods

- Published in print:
- 2010
- Published Online:
- September 2010
- ISBN:
- 9780195307238
- eISBN:
- 9780199863990
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780195307238.003.0010
- Subject:
- Neuroscience, Behavioral Neuroscience, Techniques

This chapter reviews the statistical tools available for the analysis of distributed activation maps defined either on the 2D cortical surface or throughout the 3D brain volume. Statistical analysis ... More

## Spatial Smoothing, Interactions and Geoadditive Regression

*Ludwig Fahrmeir and Thomas Kneib*

### in Bayesian Smoothing and Regression for Longitudinal, Spatial and Event History Data

- Published in print:
- 2011
- Published Online:
- September 2011
- ISBN:
- 9780199533022
- eISBN:
- 9780191728501
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199533022.003.0005
- Subject:
- Mathematics, Probability / Statistics, Biostatistics

This chapter provides an introduction to Bayesian spatial smoothing as a subject of interest in its own right, it points out the close relation between modelling interactions and spatial effects, and ... More

## Relaxor ferroelectrics

*Robert Blinc*

### in Advanced Ferroelectricity

- Published in print:
- 2011
- Published Online:
- January 2012
- ISBN:
- 9780199570942
- eISBN:
- 9780191728631
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199570942.003.0006
- Subject:
- Physics, Condensed Matter Physics / Materials

Relaxors are site‐ and charge‐disordered crystals or solid solutions where charge disorder induces random fields. They are characterized by the appearance of polar nanoclusters that are much smaller ... More

## Theory Unification and Graphical Models in Human Categorization

*David Danks*

### in Causal Learning: Psychology, Philosophy, and Computation

- Published in print:
- 2007
- Published Online:
- April 2010
- ISBN:
- 9780195176803
- eISBN:
- 9780199958511
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780195176803.003.0012
- Subject:
- Psychology, Developmental Psychology

Many different, seemingly mutually exclusive, theories of categorization have been proposed in recent years. The most notable theories have been those based on prototypes, exemplars, and causal ... More

## Ferroelectric polymers

*Robert Blinc*

### in Advanced Ferroelectricity

- Published in print:
- 2011
- Published Online:
- January 2012
- ISBN:
- 9780199570942
- eISBN:
- 9780191728631
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199570942.003.0007
- Subject:
- Physics, Condensed Matter Physics / Materials

The physical properties of ferroelectric polymers, like polyvinylidene fluoride and its copolymers are briefly discussed. It is shown that polar nanoclusters are induced either by compositional ... More

## Essentials to Understand Probabilistic Graphical Models: A Tutorial about Inference and Learning

*Christine Sinoquet*

### in Probabilistic Graphical Models for Genetics, Genomics, and Postgenomics

- Published in print:
- 2014
- Published Online:
- December 2014
- ISBN:
- 9780198709022
- eISBN:
- 9780191779619
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780198709022.003.0002
- Subject:
- Mathematics, Probability / Statistics, Biostatistics

The aim of this chapter is to offer an advanced tutorial to scientists with no background or no deep background on probabilistic graphical models. To readers more familiar with these models, this ... More

## EFFECT OF THE COULOMB INTERACTION ON THE ELECTRON ENERGY SPECTRUM

*V.F. Gantmakher*

### in Electrons and Disorder in Solids

- Published in print:
- 2005
- Published Online:
- September 2007
- ISBN:
- 9780198567561
- eISBN:
- 9780191718267
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780198567561.003.0003
- Subject:
- Physics, Condensed Matter Physics / Materials

Different examples of self-action of the electron gas onto its own energy spectrum are considered. In a regular structure, it is the Peierls transition when a minigap in the spectrum appears to ... More

## Bayesian Models for Variable Selection that Incorporate Biological Information *

*Marina Vannucci and Francesco C. Stingo*

### 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/9780199694587.003.0022
- Subject:
- Mathematics, Probability / Statistics

Variable selection has been the focus of much research in recent years. Bayesian methods have found many successful applications, particularly in situations where the amount of measured variables can ... More

## Probabilistic Graphical Models for Genetics, Genomics, and Postgenomics

*Raphaël Mourad (ed.)*

- Published in print:
- 2014
- Published Online:
- December 2014
- ISBN:
- 9780198709022
- eISBN:
- 9780191779619
- Item type:
- book

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780198709022.001.0001
- Subject:
- Mathematics, Probability / Statistics, Biostatistics

At the crossroads between statistics and machine learning, probabilistic graphical models provide a powerful formal framework to model complex data. Probabilistic graphical models are probabilistic ... More

## Gaussian multiplicative chaos and Liouville quantum gravity

*Rémi Rhodes1 and Vincent Vargas2*

### in Stochastic Processes and Random Matrices: Lecture Notes of the Les Houches Summer School: Volume 104, July 2015

- Published in print:
- 2017
- Published Online:
- January 2018
- ISBN:
- 9780198797319
- eISBN:
- 9780191838774
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/oso/9780198797319.003.0012
- Subject:
- Physics, Theoretical, Computational, and Statistical Physics

The purpose of this chapter is to explain the probabilistic construction of Polyakov’s Liouville quantum gravity using the theory of Gaussian multiplicative chaos. In particular, this chapter ... More

## Carnapian Inductive Logic for Markov Chains

*Brian Skyrms*

### in From Zeno to Arbitrage: Essays on Quantity, Coherence, and Induction

- Published in print:
- 2012
- Published Online:
- January 2013
- ISBN:
- 9780199652808
- eISBN:
- 9780191745829
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199652808.003.0014
- Subject:
- Philosophy, Philosophy of Science, Metaphysics/Epistemology

In his Nachlass, Carnap listed outstanding problems for the development of inductive logic. One was the treatment of what he called “analogy by proximity”. This can be handled naturally along ... More

## Probabilistic Semi-Supervised Clustering with Constraints

*Basu Sugato, Bilenko Mikhail, Banerjee Arindam, and Mooney Raymond*

### in Semi-Supervised Learning

- Published in print:
- 2006
- Published Online:
- August 2013
- ISBN:
- 9780262033589
- eISBN:
- 9780262255899
- Item type:
- chapter

- Publisher:
- The MIT Press
- DOI:
- 10.7551/mitpress/9780262033589.003.0005
- Subject:
- Computer Science, Machine Learning

This chapter discusses a problem resulting from certain clustering tasks from which limited supervision is obtained in the form of pairwise constraints—semi-supervised clustering. Semi-supervised ... More

## Molecular Population Genetics

*Daniel L. Hartl*

### in A Primer of Population Genetics and Genomics

- Published in print:
- 2020
- Published Online:
- August 2020
- ISBN:
- 9780198862291
- eISBN:
- 9780191895074
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/oso/9780198862291.003.0007
- Subject:
- Biology, Biomathematics / Statistics and Data Analysis / Complexity Studies, Evolutionary Biology / Genetics

Chapter 7 is an introduction to molecular population genetics that includes the principal concepts of nucleotide polymorphism and divergence, the site frequency spectrum, and tests of selection and ... More

## Detection of Copy Number Variations from Array Comparative Genomic Hybridization Data Using Linear-chain Conditional Random Field Models

*Xiaolin Yin and Jing Li*

### in Probabilistic Graphical Models for Genetics, Genomics, and Postgenomics

- Published in print:
- 2014
- Published Online:
- December 2014
- ISBN:
- 9780198709022
- eISBN:
- 9780191779619
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780198709022.003.0016
- Subject:
- Mathematics, Probability / Statistics, Biostatistics

Copy number variation (CNV) accounts for roughly 12% of the human genome. Beside their inherent role in cancer development, CNVs have been reported to underlie susceptibility to complex diseases. ... More

## Graphical Modeling of Biological Pathways in Genome-wide Association Studies

*Min Chen, Judy Cho, and Hongyu Zhao*

### in Probabilistic Graphical Models for Genetics, Genomics, and Postgenomics

- Published in print:
- 2014
- Published Online:
- December 2014
- ISBN:
- 9780198709022
- eISBN:
- 9780191779619
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780198709022.003.0012
- Subject:
- Mathematics, Probability / Statistics, Biostatistics

Genome-wide association studies (GWASs) are widely used to identify good candidates of disease-associated genes that are of interest for further follow-up studies. However, knowledge of biological ... More

## Cyclic models and recurrent neural networks

*Thomas P. Trappenberg*

### in Fundamentals of Machine Learning

- Published in print:
- 2019
- Published Online:
- January 2020
- ISBN:
- 9780198828044
- eISBN:
- 9780191883873
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/oso/9780198828044.003.0009
- Subject:
- Neuroscience, Behavioral Neuroscience

This chapter discusses models with cyclic dependencies. There are two principle architectures that are discussed. The first principle architecture of cyclic graphs comprises directed graphs similar ... More

## Statistical inference with probabilistic graphical models

*Devavrat Shah*

### in Statistical Physics, Optimization, Inference, and Message-Passing Algorithms: Lecture Notes of the Les Houches School of Physics: Special Issue, October 2013

- Published in print:
- 2015
- Published Online:
- March 2016
- ISBN:
- 9780198743736
- eISBN:
- 9780191803802
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780198743736.003.0001
- Subject:
- Physics, Theoretical, Computational, and Statistical Physics

This chapter introduces graphical models as a powerful tool to derive efficient algorithms for inference problems. When dealing with complex interdependent variables, inference problems may become of ... More

## Using Molecular Data to Detect Selection: Signatures from Multiple Historical Events

*Bruce Walsh and Michael Lynch*

### in Evolution and Selection of Quantitative Traits

- Published in print:
- 2018
- Published Online:
- September 2018
- ISBN:
- 9780198830870
- eISBN:
- 9780191868986
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/oso/9780198830870.003.0010
- Subject:
- Biology, Evolutionary Biology / Genetics, Biochemistry / Molecular Biology

This chapter examines the search for a pattern of repetitive adaptive substitutions over evolutionary time. In contrast with the previous chapter, only a modest number of tests toward this aim have ... More

## Upscaling, Computational Aspects, and Statistics of the Velocity Field

*Yoram Rubin*

### in Applied Stochastic Hydrogeology

- Published in print:
- 2003
- Published Online:
- November 2020
- ISBN:
- 9780195138047
- eISBN:
- 9780197561676
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/oso/9780195138047.003.0011
- Subject:
- Earth Sciences and Geography, Oceanography and Hydrology

This chapter deals with computing the velocity fields in heterogeneous media. This is a broad area, and we shall concentrate here on upscaling, on the spatial ... More