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Peer reviewed: True, Funder: Big Questions Institute, Annually resolved measurements of the radiocarbon content in tree-rings have revealed rare sharp rises in carbon-14 production. These ‘Miyake events’ are likely produced by rare increases in cosmic radiation from the Sun or other energetic astrophysical sources. The radiocarbon produced is not only circulated through the Earth’s atmosphere and oceans, but also absorbed by the biosphere and locked in the annual growth rings of trees. To interpret high-resolution tree-ring radiocarbon measurements therefore necessitates modelling the entire global carbon cycle. Here, we introduce ‘ ticktack ’ ( https://github.com/SharmaLlama/ticktack/ ), the first open-source Python package that connects box models of the carbon cycle with modern Bayesian inference tools. We use this to analyse all public annual 14 C tree data, and infer posterior parameters for all six known Miyake events. They do not show a consistent relationship to the solar cycle, and several display extended durations that challenge either astrophysical or geophysical models.