Where does collocation collide?

In linguistics and corpus linguistics, a collocation is a pair or cluster of words that habitually occur together more often than chance would predict, so the combination feels natural to fluent speakers: one says strong tea rather than powerful tea, though both are grammatical. Firth's 1957 A synopsis of linguistic theory gave the idea its slogan, that you shall know a word by the company it keeps, and Church and Hanks's 1990 study put numbers on it by scoring word pairs with mutual information. The referent is a statistical habit of language, a tendency for particular words to attract one another, and it is not a recipe for solving an equation, a method for mapping gravity, or a scheme for housing computer servers.[1][2]

Unit

A word pair or cluster that co-occurs above chance in a corpus

Recovery means

Not applicable

Measured by

Scored from corpus counts by association measures such as mutual information or the t-score

In numerical analysis, collocation is a method for solving a differential or integral equation approximately by writing the unknown answer as a combination of simple basis functions and then forcing the equation to hold exactly at a chosen finite set of points, the collocation points. de Boor and Swartz's 1973 Collocation at Gaussian points showed that placing those points at the Gaussian nodes of each subinterval yields unusually accurate piecewise-polynomial solutions, a result that underpins later orthogonal and spectral collocation schemes. The referent is a computational recipe for turning a continuous equation into a finite system by demanding exactness at sample points, and it has nothing to do with which words keep company, a gravity field, or a rack of servers.[3]

Unit

One approximate solution pinned to hold exactly at chosen points

Recovery means

Not applicable

Measured by

Judged by the error between the approximate and true solution, and by how it shrinks as points are added

In physical geodesy, least-squares collocation is a statistical technique for estimating the Earth's gravity field and figure by combining heterogeneous measurements, such as ground gravity readings and satellite data, into a single minimum-variance prediction of the field at points where nothing was measured. Moritz's 1978 Least-squares collocation set out the theory, in which a signal is predicted from data using its covariance structure, a construction equivalent to what statisticians call kriging or Gaussian-process prediction. The referent is a way of interpolating a continuous physical field from scattered observations, and although it shares the word with the remote-sensing method below, it is a different construct, and it has nothing to do with a habit of word co-occurrence or solving an equation at chosen points.[4]

Unit

A predicted gravity-field value at an unmeasured point, with its error

Recovery means

Not applicable

Measured by

Computed from the covariance of the observations by minimum-variance, that is least-squares, prediction

In remote sensing and geophysics, triple collocation is a method for estimating the random-error variance of three independent measurement systems that observe the same quantity, such as wind speed from a satellite, a buoy, and a model, without treating any one of them as the truth. Stoffelen's 1998 study introduced it for calibrating near-surface winds, exploiting the fact that three matched datasets supply enough equations to separate each system's noise. The referent is an error-characterisation technique that leans on matching three observations in space and time, and it differs from the geodetic prediction method, from a linguistic word habit, and from a numerical equation-solving recipe that carry the same name.[5]

Unit

An error-variance estimate for each of three co-located datasets

Recovery means

Not applicable

Measured by

Derived from the cross-covariances among three independent, spatially and temporally matched datasets