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Random field, the Glossary

In physics and mathematics, a random field is a random function over an arbitrary domain (usually a multi-dimensional space such as \mathbb^n).^[1]

44 relations: Conditional random field, Covariance, Digital elevation model, Dimension, Euclidean space, Fluid animation, Function space, Functional (mathematics), Functional magnetic resonance imaging, Functional neuroimaging, Gaussian random field, Gibbs measure, Graphical model, Integer, Interacting particle system, Ising model, Journal of the Royal Statistical Society, Julian Besag, Kriging, Look-elsewhere effect, Machine learning, Manifold, Markov property, Markov random field, Mathematics, Monte Carlo method, Multiple comparisons problem, Natural science, Neuroscience, Parameter space, Path integral formulation, Physics, Positron emission tomography, Probability space, Quantum field theory, Random variable, Real coordinate space, Representative elementary volume, Resel, Stochastic cellular automaton, Stochastic process, Topological space, Variogram, Vector space.
Spatial processes

Conditional random field

Conditional random fields (CRFs) are a class of statistical modeling methods often applied in pattern recognition and machine learning and used for structured prediction.

See Random field and Conditional random field

Covariance

Covariance in probability theory and statistics is a measure of the joint variability of two random variables.

See Random field and Covariance

A digital elevation model (DEM) or digital surface model (DSM) is a 3D computer graphics representation of elevation data to represent terrain or overlaying objects, commonly of a planet, moon, or asteroid.

See Random field and Digital elevation model

Dimension

In physics and mathematics, the dimension of a mathematical space (or object) is informally defined as the minimum number of coordinates needed to specify any point within it.

See Random field and Dimension

Euclidean space

Euclidean space is the fundamental space of geometry, intended to represent physical space.

See Random field and Euclidean space

Fluid animation

Fluid animation refers to computer graphics techniques for generating realistic animations of fluids such as water and smoke.

See Random field and Fluid animation

Function space

In mathematics, a function space is a set of functions between two fixed sets.

See Random field and Function space

Functional (mathematics)

In mathematics, a functional is a certain type of function.

See Random field and Functional (mathematics)

Functional magnetic resonance imaging

Functional magnetic resonance imaging or functional MRI (fMRI) measures brain activity by detecting changes associated with blood flow.

See Random field and Functional magnetic resonance imaging

Functional neuroimaging

Functional neuroimaging is the use of neuroimaging technology to measure an aspect of brain function, often with a view to understanding the relationship between activity in certain brain areas and specific mental functions.

See Random field and Functional neuroimaging

Gaussian random field

In statistics, a Gaussian random field (GRF) is a random field involving Gaussian probability density functions of the variables. Random field and Gaussian random field are spatial processes.

See Random field and Gaussian random field

Gibbs measure

In physics and mathematics, the Gibbs measure, named after Josiah Willard Gibbs, is a probability measure frequently seen in many problems of probability theory and statistical mechanics.

See Random field and Gibbs measure

Graphical model

A graphical model or probabilistic graphical model (PGM) or structured probabilistic model is a probabilistic model for which a graph expresses the conditional dependence structure between random variables.

See Random field and Graphical model

Integer

An integer is the number zero (0), a positive natural number (1, 2, 3,...), or the negation of a positive natural number (−1, −2, −3,...). The negations or additive inverses of the positive natural numbers are referred to as negative integers.

See Random field and Integer

Interacting particle system

In probability theory, an interacting particle system (IPS) is a stochastic process (X(t))_ on some configuration space \Omega. Random field and interacting particle system are spatial processes.

See Random field and Interacting particle system

Ising model

The Ising model (or Lenz–Ising model), named after the physicists Ernst Ising and Wilhelm Lenz, is a mathematical model of ferromagnetism in statistical mechanics.

See Random field and Ising model

Journal of the Royal Statistical Society

The Journal of the Royal Statistical Society is a peer-reviewed scientific journal of statistics.

See Random field and Journal of the Royal Statistical Society

Julian Besag

Julian Ernst Besag FRS (26 March 1945 – 6 August 2010) was a British statistician known chiefly for his work in spatial statistics (including its applications to epidemiology, image analysis and agricultural science), and Bayesian inference (including Markov chain Monte Carlo algorithms).

See Random field and Julian Besag

Kriging

In statistics, originally in geostatistics, kriging or Kriging, also known as Gaussian process regression, is a method of interpolation based on Gaussian process governed by prior covariances.

See Random field and Kriging

Look-elsewhere effect

The look-elsewhere effect is a phenomenon in the statistical analysis of scientific experiments where an apparently statistically significant observation may have actually arisen by chance because of the sheer size of the parameter space to be searched.

See Random field and Look-elsewhere effect

Machine learning

Machine learning (ML) is a field of study in artificial intelligence concerned with the development and study of statistical algorithms that can learn from data and generalize to unseen data and thus perform tasks without explicit instructions.

See Random field and Machine learning

Manifold

In mathematics, a manifold is a topological space that locally resembles Euclidean space near each point.

See Random field and Manifold

Markov property

In probability theory and statistics, the term Markov property refers to the memoryless property of a stochastic process, which means that its future evolution is independent of its history.

See Random field and Markov property

Markov random field

In the domain of physics and probability, a Markov random field (MRF), Markov network or undirected graphical model is a set of random variables having a Markov property described by an undirected graph.

See Random field and Markov random field

Mathematics

Mathematics is a field of study that discovers and organizes abstract objects, methods, theories and theorems that are developed and proved for the needs of empirical sciences and mathematics itself.

See Random field and Mathematics

Monte Carlo method

Monte Carlo methods, or Monte Carlo experiments, are a broad class of computational algorithms that rely on repeated random sampling to obtain numerical results.

See Random field and Monte Carlo method

Multiple comparisons problem

In statistics, the multiple comparisons, multiplicity or multiple testing problem occurs when one considers a set of statistical inferences simultaneously or estimates a subset of parameters selected based on the observed values.

See Random field and Multiple comparisons problem

Natural science

Natural science is one of the branches of science concerned with the description, understanding and prediction of natural phenomena, based on empirical evidence from observation and experimentation.

See Random field and Natural science

Neuroscience

Neuroscience is the scientific study of the nervous system (the brain, spinal cord, and peripheral nervous system), its functions and disorders.

See Random field and Neuroscience

Parameter space

The parameter space is the space of possible parameter values that define a particular mathematical model.

See Random field and Parameter space

Path integral formulation

The path integral formulation is a description in quantum mechanics that generalizes the stationary action principle of classical mechanics.

See Random field and Path integral formulation

Physics

Physics is the natural science of matter, involving the study of matter, its fundamental constituents, its motion and behavior through space and time, and the related entities of energy and force.

See Random field and Physics

Positron emission tomography

Positron emission tomography (PET) is a functional imaging technique that uses radioactive substances known as radiotracers to visualize and measure changes in metabolic processes, and in other physiological activities including blood flow, regional chemical composition, and absorption.

See Random field and Positron emission tomography

Probability space

In probability theory, a probability space or a probability triple (\Omega, \mathcal, P) is a mathematical construct that provides a formal model of a random process or "experiment".

See Random field and Probability space

Quantum field theory

In theoretical physics, quantum field theory (QFT) is a theoretical framework that combines classical field theory, special relativity, and quantum mechanics.

See Random field and Quantum field theory

Random variable

A random variable (also called random quantity, aleatory variable, or stochastic variable) is a mathematical formalization of a quantity or object which depends on random events.

See Random field and Random variable

Real coordinate space

In mathematics, the real coordinate space or real coordinate n-space, of dimension, denoted or, is the set of all ordered n-tuples of real numbers, that is the set of all sequences of real numbers, also known as coordinate vectors.

See Random field and Real coordinate space

Representative elementary volume

In the theory of composite materials, the representative elementary volume (REV) (also called the representative volume element (RVE) or the unit cell) is the smallest volume over which a measurement can be made that will yield a value representative of the whole.

See Random field and Representative elementary volume

Resel

In image analysis, a resel (from resolution element) represents the actual spatial resolution in an image or a volumetric dataset.

See Random field and Resel

Stochastic cellular automaton

Stochastic cellular automata or probabilistic cellular automata (PCA) or random cellular automata or locally interacting Markov chains are an important extension of cellular automaton. Random field and Stochastic cellular automaton are spatial processes.

See Random field and Stochastic cellular automaton

Stochastic process

In probability theory and related fields, a stochastic or random process is a mathematical object usually defined as a sequence of random variables in a probability space, where the index of the sequence often has the interpretation of time.

See Random field and Stochastic process

Topological space

In mathematics, a topological space is, roughly speaking, a geometrical space in which closeness is defined but cannot necessarily be measured by a numeric distance.

See Random field and Topological space

Variogram

In spatial statistics the theoretical variogram, denoted 2\gamma(\mathbf_1,\mathbf_2), is a function describing the degree of spatial dependence of a spatial random field or stochastic process Z(\mathbf). Random field and variogram are spatial processes.

See Random field and Variogram

Vector space

In mathematics and physics, a vector space (also called a linear space) is a set whose elements, often called ''vectors'', can be added together and multiplied ("scaled") by numbers called ''scalars''.

See Random field and Vector space

References

[1] https://en.wikipedia.org/wiki/Random_field

Also known as Applications of random fields, Random fields, Random-field.

Random field, the Glossary

Table of Contents

See also

Spatial processes

References