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## TYPICAL VERTEX DEGREES

*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/9780198506263.003.0004
- Subject:
- Mathematics, Probability / Statistics

This chapter is concerned with the empirical process of k-nearest neighbour distances for n random points, where k=k(n) is specified and is either fixed or grows with n. That is, the proportion of ... More

## What is a random 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/9780198567769.003.0002
- Subject:
- Physics, Theoretical, Computational, and Statistical Physics

A random or stochastic process is a random variable that evolves in time by some random mechanism (of course, the time variable can be replaced by a space variable, or some other variable, in ... More

## Gaussian Solutions

*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/9780199657063.003.0009
- Subject:
- Mathematics, Probability / Statistics, Applied Mathematics

Gaussian solutions of stochastic differential equations play a special role in linear filtering problems. After a discussion of Gohberg-Krein special factorization, its connection to Gaussian ... More

## Nonparametric Bayesian machine learning and signal processing

*Max A. Little*

### in Machine Learning for Signal Processing: Data Science, Algorithms, and Computational Statistics

- Published in print:
- 2019
- Published Online:
- October 2019
- ISBN:
- 9780198714934
- eISBN:
- 9780191879180
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/oso/9780198714934.003.0010
- Subject:
- Mathematics, Logic / Computer Science / Mathematical Philosophy, Mathematical Physics

We have seen that stochastic processes play an important foundational role in a wide range of methods in DSP. For example, we treat a discrete-time signal as a Gaussian process, and thereby obtain ... More

## Optimization Under Unknown Constraints *

*Robert B. Gramacy and Herbert K. H. Lee*

### 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/9780199694587.003.0008
- Subject:
- Mathematics, Probability / Statistics

Optimization of complex functions, such as the output of computer simulators, is a difficult task that has received much attention in the literature. A less studied problem is that of optimization ... More

## Gaussian Processes and the Null-Category Noise Model

*Lawrence Neil D. and Jordan Michael I.*

### 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/9780262033589.003.0008
- Subject:
- Computer Science, Machine Learning

This chapter presents an augmentation of the standard probabilistic classification model which incorporates a null-category. Given a suitable probabilistic model for the model category, the chapter ... More

## Gaussian Approximation under Asymptotic Negative Dependence

*Florence Merlevède, Magda Peligrad, and Sergey Utev*

### in Functional Gaussian Approximation for Dependent Structures

- Published in print:
- 2019
- Published Online:
- April 2019
- ISBN:
- 9780198826941
- eISBN:
- 9780191865961
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/oso/9780198826941.003.0009
- Subject:
- Mathematics, Probability / Statistics

Here we introduce the notion of asymptotic weakly associated dependence conditions, the practical applications of which will be discussed in the next chapter. The theoretical importance of this class ... More

## Testing for Neglected Nonlinearity Using Twofold Unidentified Models under the Null and Hexic Expansions

*Jin Seo Cho, Isao Ishida, and Halbert White*

### in Essays in Nonlinear Time Series Econometrics

- Published in print:
- 2014
- Published Online:
- August 2014
- ISBN:
- 9780199679959
- eISBN:
- 9780191760136
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199679959.003.0001
- Subject:
- Economics and Finance, Econometrics

We revisit the twofold identification problem discussed by Cho, Ishida, and White (2011), which arises when testing for neglected nonlinearity by artificial neural networks. We do not use the ... More

## Markov Random Fields On Undirected Graphs

*Ulf Grenander and Michael I. Miller*

### in Pattern Theory: From representation to inference

- Published in print:
- 2006
- Published Online:
- November 2020
- ISBN:
- 9780198505709
- eISBN:
- 9780191916564
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/oso/9780198505709.003.0005
- Subject:
- Computer Science, Programming Languages

This chapter focuses on random fields on lattices and undirected graphs. Discrete finite state spaces are examined in the context of Markov and Gibbs fields. The ... More

## Cokriging

*Vera Pawlowsky-Glahn and Richardo A. Olea*

### in Geostatistical Analysis of Compositional Data

- Published in print:
- 2004
- Published Online:
- November 2020
- ISBN:
- 9780195171662
- eISBN:
- 9780197565513
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/oso/9780195171662.003.0011
- Subject:
- Earth Sciences and Geography, Geophysics: Earth Sciences

The problem of estimation of a coregionalization of size q using cokriging will be discussed in this chapter. Cokriging—a multivariate extension of kriging—is the ... More

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