Volcanic ash is one of the farthest-reaching volcanic hazards and ash produced by large magnitude explosive eruptions has the potential to affect communities over thousands of kilometres. Quantifying the hazard from ash fall is problematic, in part because of data limitations that make eruption characteristics uncertain but also because, given an eruption, the distribution of ash is then controlled by time and altitude-varying wind conditions. Any one location may potentially be affected by ash falls from one, or a number of, volcanoes so that volcano-specific studies may not fully capture the ash fall hazard for communities in volcanically active areas. In an attempt to deal with these uncertainties, this paper outlines a probabilistic framework for assessing ash fall hazard on a regional scale. The methodology employs stochastic simulation techniques and is based upon generic principles that could be applied to any area, but is here applied to the Asia-Pacific region. Average recurrence intervals for eruptions greater than or equal to Volcanic Explosivity Index 4 were established for 190 volcanoes in the region, based upon the eruption history of each volcano and, where data were lacking, the averaged eruptive behaviour of global analogous volcanoes. Eruption histories are drawn from the Smithsonian Institution's Global Volcanism Program catalogue of Holocene events and unpublished data, with global analogues taken from volcanoes of the same type category: Caldera, Large Cone, Shield, Lava dome or Small Cone. Simulated are 190,000 plausible eruption scenarios, with ash dispersal for each determined using an advection-diffusion model and local wind conditions. Key uncertainties are described by probability distributions. Modelled results include the annual probability of exceeding given ash thicknesses, summed over all eruption scenarios and volcanoes. A companion paper describes the results obtained for the Asia-Pacific region.