We describe a new method for the reconstruction (or forecast) of probabilities that distal geographic locations were inundated by a large pyroclastic density current (PDC) in terms of the flow mass and related uncertainties. Using appropriate model input uncertainty distributions, derived from expert judgements using the equal weights combination rule, we can estimate the mass amount needed to reach a marginal locality at any given confidence level and compare this with ambiguous or inexact peripheral field data. Our analysis relies on different versions of the Huppert and Simpson (1980) integral formulation of axisymmetric gravity-driven particle currents. We focus on models which possess analytical solutions, enabling us to utilize a very fast functional approach for enumerating results and uncertainties. In particular, we adapt the ‘energy conoid’ approach to generate inundation maps along radial directions, based on comparison of the mass-dependent kinetic energy of the flow with the potential energy control by topography in the direction of flow at distal ranges. We focus on two alternative conceptual models: (i) Model 1 assumes the entire amount of solid material originates from a prescribed height above the volcano and flows as a granular current slowed by constant friction; (ii) Model 2 is a multi-phase formulation and includes, in addition to suspended particles, interstitial gas thermally buoyant with respect to surrounding cold air. In the latter case, the flow stops propagating at the surface when the solid fraction becomes less than a critical value, and there is lift-off of the remaining mixture of gas and small particulates. Our model parameters can be further constrained where there is reliable field data or information from analogue eruptions. Finally, we used a Bayes Belief Network related to each inversion model to evaluate probabilistically the uncertainties on the mass required, estimating correlation coefficients between input variables and the calculated mass. For any major magnitude ignimbrite PDC scenario, our method provides a rational basis for assessing the probability of distal flow inundation at critical peripheral locations when there is major uncertainty about the actual or predicted extent of flow runout. Example case histories are illustrated.