A Unified Framework for Bayesian and Non-Bayesian Decision Making and Inference
Bibliographic record
Abstract
After showing, by means of a series of examples, that paradigms alternative to the Bayesian one obtain by simply replacing the notion of approximation associated with the latter, the paper presents a unified framework for theories of decision making and inference. Given a statistical model, the algebra of bounded random variables on the sample space is mapped homomorphically into an algebra of operators on a certain Hilbert space. Then, the choice of a norm or a divergence function on the latter algebra produces a theory of decision making and inference. Examples include models from the Choquet expected utility class, models from robust statistics, the smooth model, maxmin and maxmax (as limiting cases) as well as a novel theory. The paper also contributes to Bayesian theory, which obtains in correspondence to a Hilbert norm. It shows that Bayes’ theorem can be derived from the fundamental concept of conditional expectation and that it is the only updating rule for which the operations of updating and of calculating the predictive commute.
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.
How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.013 | 0.014 |
| Meta-epidemiology (narrow) | 0.002 | 0.001 |
| Meta-epidemiology (broad) | 0.002 | 0.003 |
| Bibliometrics | 0.003 | 0.003 |
| Science and technology studies | 0.002 | 0.007 |
| Scholarly communication | 0.006 | 0.008 |
| Open science | 0.004 | 0.004 |
| Research integrity | 0.004 | 0.007 |
| Insufficient payload (model declined to judge) | 0.005 | 0.001 |
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.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from itClassification
machine, unvalidatedMachine predicted; a candidate call from one source (direct Gemma or distilled Codex), not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".