Abstract Eruption source parameters (ESPs) used to characterize explosive eruptions are estimated from tephra deposit data using different models (statistical or numerical) and inversion approaches. The ESPs thus derived are subject to substantial uncertainties when the bulk of the tephra deposit, including information about its full spatial extent and spatial variation in grain-size distribution is missing due to geographical and environmental conditions. We use an advection–diffusion model coupled with a Bayesian inversion and uncertainty quantification algorithm to investigate how ESPs can be robustly estimated given such conditions. The 2021 eruption of La Soufrière volcano (St Vincent and the Grenadines) is our case study. An inversion is conducted for the first two explosive phases of this eruption (U1 and U2). We estimate: an erupted mass of 3.3 × 10 10 ± 1 × 10 10 kg for U1 and 3.1 × 10 10 ± 1.9 × 10 9 kg for U2, with an average particles release height of c. 13.5 km a.s.l. ±0.5 km for both phases. Given the efficiency of the proposed approach and the plausibility of the stochastic inversion results, we recommend this procedure for estimating ESPs for explosive eruptions for which the bulk of the deposit is missing or is inaccessible.