Quantifying the Bayesian Evidence for a Planet in Radial Velocity Data
Bibliographic record
Abstract
Abstract We present results from a data challenge posed to the radial velocity (RV) community: namely, to quantify the Bayesian “evidence” for n = {0, 1, 2, 3} planets in a set of synthetically generated RV data sets containing a range of planet signals. Participating teams were provided the same likelihood function and set of priors to use in their analysis. They applied a variety of methods to estimate , the marginal likelihood for each n -planet model, including cross-validation, the Laplace approximation, importance sampling, and nested sampling. We found the dispersion in across different methods grew with increasing n -planet models: ∼3 for zero planets, ∼10 for one planet, ∼10 2 –10 3 for two planets, and >10 4 for three planets. Most internal estimates of uncertainty in for individual methods significantly underestimated the observed dispersion across all methods. Methods that adopted a Monte Carlo approach by comparing estimates from multiple runs yielded plausible uncertainties. Finally, two classes of numerical algorithms (those based on importance and nested samplers) arrived at similar conclusions regarding the ratio of for n- and ( n + 1)-planet models. One analytic method (the Laplace approximation) demonstrated comparable performance. We express both optimism and caution: we demonstrate that it is practical to perform rigorous Bayesian model comparison for models of ≤3 planets, yet robust planet discoveries require researchers to better understand the uncertainty in and its connections to model selection.
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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 | 0.042 | 0.202 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.003 | 0.002 |
| Science and technology studies | 0.001 | 0.003 |
| Scholarly communication | 0.005 | 0.005 |
| Open science | 0.002 | 0.004 |
| Research integrity | 0.002 | 0.002 |
| Insufficient payload (model declined to judge) | 0.001 | 0.000 |
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".