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The high precision and conformity of intensity-modulated particle therapy(IMPT) comes at the cost of susceptibility to treatment uncertainties inparticle range and patient set-up. Dose uncertainty quantification andmitigation, which is usually based on sampled error scenarios, however becomeschallenging when computing the dose with computationally expensive but accurateMonte Carlo (MC) simulations. This paper introduces an importance(re-)weighting method in MC history scoring to concurrently construct estimatesfor error scenarios, the expected dose and its variance from a single set of MCsimulated particle histories. The approach relies on a multivariate Gaussianinput and uncertainty model, which assigns probabilities to the initial phasespace sample, enabling the use of different correlation models. Exploring andadapting bivariate emittance parametrizations for the beam shape, accuracy canbe traded between that of the uncertainty or the nominal dose estimate. Themethod was implemented using the MC code TOPAS and tested for proton IMPT plandelivery in comparison to a reference scenario estimate. We achieve accurateresults for set-up uncertainties ($\gamma_{3mm/3\%} \geq 99.99\%$) andexpectedly lower but still sufficient agreement for range uncertainties, whichare approximated with uncertainty over the energy distribution ($\gamma_{3mm/3\%} \geq 99.50\%$ ($E[\boldsymbol{d}]$), $\gamma_{3mm/3\%} \geq 91.69\%$($\sigma(\boldsymbol{d})$) ). Initial experiments on a water phantom, aprostate and a liver case show that the re-weighting approach lowers the CPUtime by more than an order of magnitude. Further, we show that uncertaintyinduced by interplay and other dynamic influences may be approximated usingsuitable error correlation models.

Efficient uncertainty quantification for Monte Carlo dose calculations using importance (re-)weighting