We review results from QCD axion string and domain wall simulations and propagate the associated uncertainties into the calculation of the axion relic density. This allows us to compare different results in the literature and, using cosmological constraints, to perform statistical inference on the axion mass window in the post-inflationary Peccei-Quinn symmetry breaking scenario. For dark matter axions, this leads to a median dark matter axion mass of 0.50 meV, while the 95% credible interval at highest posterior density is between 0.48 and 0.52 meV. For simulations including string-domain wall decays, these numbers are 0.22 meV and [0.16, 0.27] meV. Relaxing the condition that axions are all of the dark matter, the axion mass window is completed by an upper bound of around 80 meV, which comes from hot dark matter constraints. This demonstrates, at least from the statistical perspective, that the axion mass can be constrained rather precisely once it is possible to overcome the much larger systematic uncertainties.
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