Deconstructing overdispersion: a generative variance budget for luminescence dating from single grains to aliquots

Overdispersion, the spread of equivalent-dose estimates beyond their measurement uncertainties, is the most reported and least interpretable number in luminescence dating: grain response, beta-dose heterogeneity, incomplete bleaching, mixing, fading, saturation, and understated errors produce the same value. Rebuilt from its physics as a variance budget, it yields four findings. Correlated intrinsic and dose-rate variance cannot be resolved from one dose distribution without an independent constraint. A boundary-calibrated test improves routine practice, but the detectable overdispersion falls only as \(n-1/4\) with grain count n : most published datasets cannot resolve a modest real dispersion, and a realistic instrumental floor nearly doubles the limit. Log-dose skewness separates added-dose from loss mechanisms, yet co-acting mechanisms and a natively skewed dose-rate field mimic either, so shape statistics are prompts, not classifiers. Multi-grain averaging divides the diagnosable dispersion by an effective grain number, about eight for fifty bright-dominated grains, but leaves additive bias in place: a clean aliquot is not a clean sample. Read without these limits, a dispersion value credits an age to a mechanism the data cannot support; which mechanism acted is a measurement question, not a computational one. The framework matches reference software to 0.01 percentage points on published quartz datasets.