regression
The same patients, measured again and again
It is the era of longitudinal medicine, and you have blood-pressure readings taken monthly from hundreds of patients — but the repeated measurements on one patient are correlated, and a regression that treats every reading as an independent observation will drastically overstate its own certainty. Model the structure honestly: a population-level trend plus patient-specific random deviations, so each person can have their own baseline and slope drawn from a shared distribution. Get it wrong and you either pool everyone and erase real individual differences, or fit a separate line per patient and drown in noise — and, worst, you report confidence intervals far too narrow because you counted correlated readings as independent, and a treatment effect looks certain when it is not.
Who this problem belongs to
The two figures whose methods fit it best, out of 66 in contention.
Gelman's career-defining contribution is hierarchical Bayesian modeling — exactly the 'population-level trend plus patient-specific random deviations drawn from a shared distribution' this problem asks for, formalized with real rigor and made practically fittable through the Stan software he helped build. His textbooks give the clearest modern account of why pooling every patient's readings as independent overstates certainty, and why partial pooling toward a population mean, letting each patient have their own baseline and slope shrunk appropriately, is the honest solution. His applied Bayesian workflow was developed specifically for longitudinal and repeated-measures data like blood-pressure readings across many patients. His work arrives decades after this problem's era-agnostic setting, but no other figure engages this exact structure more directly or completely.
Fisher's 1918 paper 'The Correlation Between Relatives on the Supposition of Mendelian Inheritance' introduced the variance-components idea — partitioning total variability into distinct sources, one of which is a random, population-level source rather than a fixed effect — which is the conceptual seed of the random-effects structure this repeated-measures problem requires. His analysis of variance framework more broadly gave the field its first rigorous tools for handling grouped, non-independent data. But Fisher's own random-effects work centered on genetics rather than longitudinal repeated measurement, and the specific mixed-model machinery for correlated readings on the same patient over time was developed by others building on his variance-components foundation decades later. His broader legacy in variance decomposition shaped the diagnostic vocabulary later mixed-model theorists inherited directly.
Fought here
In the mind map
The same ideas, as concepts rather than history — in John's ML knowledge map.
66 figures are scored on this problem. Draw it in a battle to see where you land.