Editing Random field (section)

== Applications ==
When used in the [[natural sciences]], values in a random field are often spatially correlated. For example, adjacent values (i.e. values with adjacent indices) do not differ as much as values that are further apart. This is an example of a [[covariance]] structure, many different types of which may be modeled in a random field. One example is the [[Ising model]] where sometimes nearest neighbor interactions are only included as a simplification to better understand the model.

A common use of random fields is in the generation of computer graphics, particularly those that mimic natural surfaces such as [[Fluid simulation|water]] and [[Digital terrain model|earth]]. Random fields have been also used in subsurface ground models as in <ref>{{cite journal|last1= Cardenas |first1=IC|title= A two-dimensional approach to quantify stratigraphic uncertainty from borehole data using non-homogeneous random fields|journal=Engineering Geology|date=2023|doi=10.1016/j.enggeo.2023.107001|doi-access=free}}</ref>

In [[neuroscience]], particularly in [[Functional neuroimaging|task-related functional brain imaging]] studies using [[Positron emission tomography|PET]] or [[Functional magnetic resonance imaging|fMRI]], statistical analysis of random fields are one common alternative to [[Multiple comparisons problem|correction for multiple comparisons]] to find regions with ''truly'' significant activation.<ref>{{Cite journal|last=Worsley|first=K. J.|last2=Evans|first2=A. C.|last3=Marrett|first3=S.|last4=Neelin|first4=P.|date=November 1992|title=A Three-Dimensional Statistical Analysis for CBF Activation Studies in Human Brain|journal=Journal of Cerebral Blood Flow & Metabolism|language=en-US|volume=12|issue=6|pages=900–918|doi=10.1038/jcbfm.1992.127|pmid=1400644|issn=0271-678X|doi-access=free}}</ref> More generally, random fields can be used to correct for the [[look-elsewhere effect]] in statistical testing, where the domain is the [[parameter space]] being searched.<ref>    {{cite journal |last1=Vitells |first1=Ofer |last2=Gross |first2=Eilam |date=2011 |title=Estimating the significance of a signal in a multi-dimensional search |journal=Astroparticle Physics |volume=35 |pages=230-234 |doi=10.1016/j.astropartphys.2011.08.005 |arxiv=1105.4355}}</ref>

They are also used in [[machine learning]] applications (see [[graphical model]]s).