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Record W3174289447 · doi:10.1201/9780429341731-10

The Tangent Exponential Model

2024· book-chapter· en· W3174289447 on OpenAlex

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

Venuenot available
Typebook-chapter
Languageen
FieldMathematics
TopicStatistical Methods and Bayesian Inference
Canadian institutionsUniversity of Toronto
Fundersnot available
KeywordsTangentExponential functionMathematicsMathematical analysisGeometry

Abstract

fetched live from OpenAlex

In a series of papers starting in the late 1980s, D. A. S. Fraser, N. Reid and coworkers developed the tangent exponential model for higher-order likelihood inference. This chapter aims to explain the motivation and justification for this model and to describe how it is used to compute accurate approximations. The literature on this is not entirely transparent, as the argument evolved over numerous articles (Fraser, 1988, 1990, 1991, 2004; Fraser and Reid, 1988, 1993, 1995, 2001; Cakmak et al., 1994; Fraser et al., 1999). We give a heuristic account of this construction, for the most part skating over the technical details, and provide an annotated bibliography as a road map through the literature. The high accuracy of the resulting approximations has been verified empirically both in numerous articles and in books such as Brazzale et al. (2007), Chapter 8 of which overlaps with the account here.

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 categoriesInsufficient payload (model declined to judge)
Consensus categoriesnone
DomainCandidate signal: none · Consensus signal: none
Study designCandidate signal: Theoretical or conceptual · Consensus signal: Theoretical or conceptual
GenreCandidate signal: Other · Consensus signal: Other
Teacher disagreement score0.147
Threshold uncertainty score0.999

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)0.0020.001

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 head0.114
GPT teacher head0.371
Teacher spread0.257 · 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