The method of forced probabilities: a computation trick for Bayesian model evidence
Bibliographic record
Abstract
Abstract Bayesian model selection objectively ranks competing models by computing Bayesian Model Evidence (BME) against test data. BME is the likelihood of data to occur under each model, averaged over uncertain parameters. Computing BME can be problematic: exact analytical solutions require strong assumptions; mathematical approximations (information criteria) are often strongly biased; assumption-free numerical methods (like Monte Carlo) are computationally impossible if the data set is large, for example like high-resolution snapshots from experimental movies. To use BME as ranking criterion in such cases, we develop the “Method of Forced Probabilities (MFP)”. MFP swaps the direction of evaluation: instead of comparing thousands of model runs on random model realizations with the observed movie snapshots, we force models to reproduce the data in each time step and record the individual probabilities of the model following these exact transitions. MFP is fast and accurate for models that fulfil the Markov property in time, paired with high-quality data sets that resolve all individual events. We demonstrate our approach on stochastic macro-invasion percolation models that simulate gas migration in porous media, and list additional examples of probable applications. The corresponding experimental movie was obtained from slow gas injection into water-saturated, homogeneous sand in a 25 x 25 x 1 cm acrylic glass tank. Despite the movie not always satisfying the high demands (resolving all individual events), we can apply MFP by suggesting a few workarounds. Results confirm that the proposed method can compute BME in previously unfeasible scenarios, facilitating a ranking among competing model versions for future model improvement.
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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 | 0.009 | 0.048 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.002 |
| Bibliometrics | 0.004 | 0.002 |
| Science and technology studies | 0.001 | 0.002 |
| Scholarly communication | 0.003 | 0.004 |
| Open science | 0.003 | 0.004 |
| Research integrity | 0.002 | 0.005 |
| Insufficient payload (model declined to judge) | 0.008 | 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".