Non-linearity in Bayesian 1-D magnetotelluric inversion
Bibliographic record
Abstract
This paper applies a Bayesian approach to examine non-linearity for the 1-D magnetotelluric (MT) inverse problem.In a Bayesian formulation the posterior probability density (PPD), which combines data and prior information, is interpreted in terms of parameter estimates and uncertainties, which requires optimizing and integrating the PPD.Much work on 1-D MT inversion has been based on (approximate) linearized solutions, but more recently fully non-linear (numerical) approaches have been applied.This paper directly compares results of linearized and non-linear uncertainty estimation for 1-D MT inversion; to do so, advanced methods for both approaches are applied.In the non-linear formulation used here, numerical optimization is carried out using an adaptive-hybrid algorithm.Numerical integration applies Metropolis-Hastings sampling, rotated to a principal-component parameter space for efficient sampling of correlated parameters, and employing non-unity sampling temperatures to ensure global sampling.Since appropriate model parametrizations are generally not known a priori, both under-and overparametrized approaches are considered.For underparametrization, the Bayesian information criterion is applied to determine the number of layers consistent with the resolving power of the data.For overparametrization, prior information is included which favours simple structure in a manner similar to regularized inversion.The data variance and/or trade-off parameter regulating data and prior information are treated in several ways, including applying fixed optimal estimates (an empirical Bayesian approach) or including them as hyperparameters in the sampling (hierarchical Bayesian).The latter approach has the benefit of accounting for the uncertainty in the hyperparameters in estimating model parameter uncertainties.Non-linear and linearized inversion results are compared for synthetic test cases and for the measured COPROD1 MT data by considering marginal probability distributions and marginal profiles.In some cases, important differences are indicated, including poorer sensitivity to thin and/or low-conductivity layers for linearized inversion, and multimodal PPDs which cannot be addressed within a linearized approach.
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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 | 0.004 | 0.012 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.000 | 0.002 |
| Scholarly communication | 0.001 | 0.002 |
| Open science | 0.001 | 0.002 |
| Research integrity | 0.001 | 0.001 |
| 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".