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Uncertainty quantification (UQ) in eruption source parameters, like tephra volume, plume height, and umbrella cloud radius, is a challenge for volcano scientists because tephra deposits are often sparsely sampled due to burial, erosion, and related factors. We find that UQ is improved by coupling an advection‐diffusion model with two Bayesian inversion approaches: (a) a robust but computationally expensive Generalized Likelihood Uncertainty Estimation algorithm, and (b) a more approximate but inexpensive parameter estimation algorithm combined with first‐order, second‐moment uncertainty estimation. We apply the two inversion methods to one sparsely sampled tephra fall unit from the 2070 BP El Misti (Peru) eruption and obtain: Tephra mass 0.78–1.4 × 1011 kg; umbrella cloud radius 4.5–16.5 km, and plume height 8–35 km (95% confidence intervals). These broad ranges demonstrate the significance of UQ for eruption classification based on mapped deposits, which has implications for hazard management. Plain Language Summary: Volcanologists use ashfall deposits to estimate the magnitudes and intensities of past or unobserved eruptions. Different processes can affect the ash deposits during and after the eruption (e.g., burial, remobilisation, and erosion) resulting in sparse sampling of the deposit and uncertainty in the deposit thickness where it is sampled. Uncertain data results in uncertain estimates of erupted volume, plume height, and umbrella cloud dimensions, which are essential parameters used to estimate future volcanic hazards. Here we present two methods to quantify the uncertainty in these parameter estimates from deposit data. As a case study, we estimate eruption parameters for a sparsely sampled ashfall deposit from the 2070 BP eruption of El Misti, Peru. We find that for this sampled unit the mass of the erupted tephra was 0.78–1.4 × 1011 kg, umbrella cloud radius was 4.5–16.5 km, and plume height was 8–35 km. These ranges are 95% confidence intervals, giving a much better idea of the eruption magnitude and intensity than that is achieved from point estimates, such as reporting the erupted mass as a single value. Key Points: Characterising volcanic eruptions based on incompletely preserved and sampled tephra deposits leads to uncertainty in classificationWe couple a tephra forward model to two inversion techniques to quantify eruption parameter uncertaintyResults show uncertainty quantification is crucial for sparsely sampled deposits because range in eruption parameters can be substantial [ABSTRACT FROM AUTHOR]