Statistical fallibility and the longevity of popes: William Farr meets Wilhelm Lexis
Bibliographic record
Abstract
We write to follow up on the editorial1 on the use of statistical aggregates. We focus on the reaction, in it, to the letter from two of us (MPC and DS) in the same issue suggesting that the ‘longer (average) life expectancy of popes relative to artists2 reflects the lives characterized by social instability, high-risk behaviours and geographical mobility (and thus infection risk) of the artists.’ The Editorial presented evidence that the ‘assumption of better behaviour by the popes is perhaps unjustified’. We have now looked behind the summary longevity statistics, and present individualized data showing that the initial, but tentative, conclusion about their longer life expectancy should be reversed. Even if the assumption of better behaviour ‘on average’ of popes is justified, these behaviours were not—even on average—accompanied by longer life expectancy. We now show the longevity data in Figure 1, using the Lexis diagram,3 a device sadly neglected by modern epidemiologists. It plots advancing age on the vertical, and calendar time on the horizontal, axis. The ‘pope-years’ (i.e. after they were elected) are shown in black and the artist-years (all of them) in grey. In the initial report, the statistics, aggregated over centuries, suggested that popes had a longevity advantage of several years. However, if we proceed papacy by papacy, the inter-ocular traumatic test4 (IOTT)—another under-used analytic device—applied to Figure 1 reveals that among those who were alive at the age at which each papacy commenced, the average remaining life of the popes was shorter than that of the corresponding peer artists—at least up until 1750 or so, after which the distributions became more similar.
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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 | 0.024 | 0.149 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.002 | 0.001 |
| Bibliometrics | 0.003 | 0.002 |
| Science and technology studies | 0.003 | 0.009 |
| Scholarly communication | 0.006 | 0.011 |
| Open science | 0.003 | 0.004 |
| Research integrity | 0.026 | 0.035 |
| Insufficient payload (model declined to judge) | 0.019 | 0.013 |
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".