Bayesian hierarchical modelling of noisy spatial rates on a modestly large and discontinuous irregular lattice
Why this work is in the frame
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Bibliographic record
Abstract
We present Bayesian hierarchical spatial model development motivated from a recent analysis of noisy small area response rate data, named the Booster data. The Booster data are postcode-level aggregates from a recent mail-out recruitment for a physical exercise intervention in deprived urban neighbourhoods in Sheffield, UK. Bayesian hierarchical Bernoulli-binomial spatial mixture zero-inflated Binomial models were developed for modelling overdispersion and for separation of systematic and random variations in the noisy and mostly low crude response rates. We present methods that enabled us to explore the underlying spatial rate variation, clustering of low or high response rate areas and neighbourhood characteristics that were associated with variations and patterns of invitation mail-outs, zero-response and response rates. Three spatial prior formulations, the intrinsic conditional autoregressive or (iCAR), the Besag-York-Mollié (BYM) and the modified BYM models, were explored for their performance on modelling sparse data on a modestly large and discontinuous irregular lattice. An in-depth Bayesian analysis of the Booster data is presented, with the resulting posterior estimation and inference implemented via Markov chain Monte Carlo simulation in WinBUGS. With increasing availability of spatial data referenced at fine spatial scales such as the postcode, the sparse-data situation and the Bayesian models and methods discussed herein should have considerable relevance to small area disease and health mapping and to spatial regression.
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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 | 0.028 | 0.138 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.000 |
| Bibliometrics | 0.000 | 0.001 |
| Science and technology studies | 0.000 | 0.002 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.001 | 0.000 |
| Research integrity | 0.000 | 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 it