regression
Counting accidents
It is the 1970s, and an insurer must model how many claims a policy generates per year as a function of the driver's characteristics — but claim counts are small non-negative integers, often zero, and forcing a straight-line regression on them predicts negative accidents and mismodels a variance that grows with the mean. Fit a regression built for counts, linking a linear predictor to the log of an expected rate under a distribution suited to rare events, and interpret the multiplicative effects. Get it wrong and premiums are set on predicted claim counts that are negative or whose uncertainty is badly miscalibrated — and the same count-regression machinery, gotten right, underlies everything from epidemiology's case rates to the modeling of website clicks.
Who this problem belongs to
The two figures whose methods fit it best, out of 70 in contention.
Cox's foundational work establishing the generalized linear model framework, alongside his 1958 logistic-regression paper, supplied the conceptual architecture — linking a linear predictor to a distribution's mean through a chosen link function — that Nelder and Wedderburn formalized in 1972 specifically to unify models like this one, where an insurer must relate claim counts to driver characteristics through a log link and a distribution suited to rare, non-negative integer events. His deep engagement with exactly this style of regression, and his collaborations on point-process and count-data models, put him at the direct center of the tradition this problem requires. He did not author the specific Poisson-regression paper, but the framework making it coherent is substantially his, developed in exactly this period.
Neyman's 1939 paper on contagious distributions was written specifically to model accident statistics — the observation that some individuals are more accident-prone than others, producing count data that a simple Poisson model underdisperses — making this problem almost literally Neyman's own applied research. His Neyman Type A distribution and his broader work on modeling heterogeneous count processes anticipate exactly the insurer's difficulty in this scenario: claim counts vary by driver in ways a naive single-rate model cannot capture. His hypothesis-testing framework further supplies the rigor needed to validate such a model honestly. He predates the specific log-link GLM formalism by decades, but his substantive statistical target is this problem's target, worked on directly and by name.
In the mind map
The same ideas, as concepts rather than history — in John's ML knowledge map.
70 figures are scored on this problem. Draw it in a battle to see where you land.