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Record W1532213635 · doi:10.1002/9780470057339.var008

Random Field, Gaussian

2006· other· en· W1532213635 on OpenAlex
Keith J. Worsley

Why this work is in the frame

A frame that forgets how it found something cannot be audited. These are the routes that admitted this work.

affAt least one author lists a Canadian institution in the pinned OpenAlex snapshot.

Bibliographic record

VenueEncyclopedia of Environmetrics · 2006
Typeother
Languageen
FieldEnvironmental Science
TopicSoil Geostatistics and Mapping
Canadian institutionsMcGill University
Fundersnot available
KeywordsGaussian random fieldGaussianMathematicsRandom fieldCovariance functionMultivariate random variableMultivariate normal distributionMultivariate t-distributionGaussian processCombinatoricsMultivariate statisticsCovarianceRandom variableStatisticsPhysics

Abstract

fetched live from OpenAlex

Abstract The Gaussian random field Y ( t ), t ∈ T , is one of the most common models used to describe spatial stochastic processes. In many applications, the domain T is a subset of D ‐dimensional Euclidean space (usually D = 2 or D = 3), and the function Y ( t ) is almost surely continuous or smooth in t . The definition is simple: the Gaussian random field must be multivariate Gaussian at all finite sets of points, that is, [ Y ( t 1 ), …, Y ( t n )] must be multivariate Gaussian for all n > 0 and all t j ∈ T . Since the multivariate Gaussian is specified uniquely by its mean vector and variance matrix, then the Gaussian random field is defined uniquely by its mean function μ ( t ) = E[ Y ( t )] and its covariance function C ( s , t ) = cov[ Y ( s ), Y ( t )].

Fetched live from OpenAlex and de-inverted. Abstracts are not stored in this database: the inverted indexes are 8.6 GB of the frame’s 9.3 GB of text, and the host has 13 GB free.

Full frame distilled prediction

Teacher imitation

Not calibrated prevalence, not ground truth. Human validation pending. Learned from the 10,348 direct Codex labels and 10,348 direct Gemma labels. Candidate is the union of thresholded teacher heads; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels or direct frontier model labels.

metaresearch head score (Codex)0.000
metaresearch head score (Gemma)0.000
Version: codex-gemma-dda1882f352aValidation status: machine_predicted_unvalidated
Candidate categoriesMeta-epidemiology (narrow), Insufficient payload (model declined to judge)
Consensus categoriesInsufficient payload (model declined to judge)
DomainCandidate signal: none · Consensus signal: none
Study designCandidate signal: Not applicable · Consensus signal: Not applicable
GenreCandidate signal: Other · Consensus signal: Other
Teacher disagreement score0.028
Threshold uncertainty score1.000

Codex and Gemma teacher scores by category

CategoryCodexGemma
Metaresearch0.0000.000
Meta-epidemiology (narrow)0.0000.000
Meta-epidemiology (broad)0.0000.000
Bibliometrics0.0000.000
Science and technology studies0.0000.000
Scholarly communication0.0000.000
Open science0.0000.000
Research integrity0.0000.000
Insufficient payload (model declined to judge)0.0140.001

Machine scores (provisional)

The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.

Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.

Opus teacher head0.005
GPT teacher head0.203
Teacher spread0.198 · how far apart the two teachers sit on this one work
Validation statusscore_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from it