Forecasts of future volcanic activity are frequently required for volcanic fields as their relatively low eruption rates and fertile soils draw human populations to live in close proximity to these potentially hazardous regions. Harrat Rahat in the Kingdom of Saudi Arabia is one of these volcanic fields, situated immediately south east of the city of Al-Madinah (population 1.5 million). Recent eruptions (641 AD, 1256 AD) and a seismic swarm (1999 AD) motivated this research to model past and potential volcanic activity within Harrat Rahat. The complexity of volcanic systems, the difficulty of establishing precise event records, and ignorance of the specific subsurface processes driving volcanic eruptions render deterministic approaches currently, and potentially never, unattainable. Thus, the majority of existing approaches to hazard forecasting are probabilistic, in which patterns are fitted to previous activity and then extrapolated into the future. To forecast activity in volcanic systems, some simplification is required to attempt to model their behaviour. These include the assumptions of independent spatial and temporal behaviour, and that each eruption centre is a separate eruption in both time and space. However, the choice of simplification approach has the potential to render incorrect, rather than just uncertain, results. Novel quantitative methods were developed to address three major complexities noted within volcanic fields: (1) multiple-vent eruptions, (2) hidden eruptive centres, and (3) the relationship of volcanism to geological, geophysical, and geographical ancillary data. Sensitivity analyses were then completed for two major subjective decisions common during volcanic field hazard forecasting: (1) the definition of a volcanic field boundary, and (2) selection of a pattern approximation method. Application of these new techniques to Harrat Rahat resulted in a conservative forecast for future eruption activity. This forecast incorporates the complex, multi-dimensional eruptions noted within Harrat Rahat by collapsing the 968 identified vents into 752 events and is based on an anisotropic kernel spatial smoothing method with an expanding volcanic field boundary. However, substantial uncertainties are attached to this forecast due predominantly to insufficient age data for the field. Ancillary data analysis also revealed structural controls on the volcanism across the Arabian Shield suggesting that future work should be focussed both on age data collection and geophysical methods to reveal crustal structure. This work also raises questions concerning a large number of existing practices in volcanic hazard forecasting, especially with regards to objective decision-making and assumption validation. An open, defensible procedure is suggested as a first step towards a consolidated process for the development of hazard forecasts.