On the detection of Lorentzian profiles in a power spectrum: a Bayesian approach using ignorance priors
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Bibliographic record
Abstract
<i>Aims. <i/>Deriving accurate frequencies, amplitudes, and mode lifetimes from stochastically driven pulsation is challenging, more so, if one demands that realistic error estimates be given for all model fitting parameters. As has been shown by other authors, the traditional method of fitting Lorentzian profiles to the power spectrum of time-resolved photometric or spectroscopic data via the maximum likelihood estimation (MLE) procedure delivers good approximations for these quantities. We, however, show that a conservative Bayesian approach allows one to treat the detection of modes with minimal assumptions (i.e., about the existence and identity of the modes).<i>Methods. <i/>We derive a conservative Bayesian treatment for the probability of Lorentzian profiles being present in a power spectrum and describe an efficient implementation that evaluates the probability density distribution of parameters by using a Markov-chain Monte Carlo (MCMC) technique.<i>Results. <i/>Potentially superior to “best-fit” procedure like MLE, which only provides formal uncertainties, our method samples and approximates the actual probability distributions for all parameters involved. Moreover, it avoids shortcomings that make the MLE treatment susceptible to the built-in assumptions of a model that is fitted to the data. This is especially relevant when analyzing solar-type pulsation in stars other than the Sun where the observations are of lower quality and can be over-interpreted. As an example, we apply our technique to CoRoT (<i>COnvection, ROtation and planetary Transits<i/> space mission, launched on 2006 December 27, was developed and is operated by the CNES, with participation of the Science Programs of ESA, ESAs RSSD, Austria, Belgium, Brazil, Germany and Spain.) observations of the solar-type pulsator HD 49933.
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Full frame distilled prediction
Teacher imitationNot 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.
Codex and Gemma teacher scores by category
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.000 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.000 | 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 it