Basis function choice for trans-dimensional models in geophysical inference
Bibliographic record
Abstract
Inference methods depend on parametrization choices. Over-parametrized, under-parametrized, and trans-dimensional (trans-D) models are routinely chosen. Over-parametrization employs space discretization below the resolution power of the data and includes regularization (e.g. Tikhonov) to control the amount of model structure. Under-parametrized models employ fewer parameters, and practitioners choose model complexity (e.g. the number of seabed layers) that is consistent with data information, often based on incomplete prior information. Trans-D models assign model complexity based on data information in an automated, data-driven procedure. The success of trans-D models depends on the choice of basis function for space partitioning. We review existing trans-D approaches and present new ones for 2D and 3D Earth models. Existing approaches include Voronoi partitioning, wavelet decomposition, and polynomial shapes, which can produce inadequate results. New approaches use various degrees of prior information when assigning the basis. The approaches include multiple nested Voronoi diagrams, a combination of grid data and alpha shapes, and partitioning of Voronoi diagrams with horizontal and vertical lines and planes. Since the computational burden is significant for 2D and 3D Earth models, we study various algorithms to carry out partitioning and show that approximate nearest neighbours are sufficiently accurate and outperform other methods.
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 | 0.006 | 0.020 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.002 |
| Bibliometrics | 0.002 | 0.002 |
| Science and technology studies | 0.001 | 0.002 |
| Scholarly communication | 0.002 | 0.003 |
| Open science | 0.002 | 0.003 |
| Research integrity | 0.002 | 0.004 |
| Insufficient payload (model declined to judge) | 0.002 | 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".