Abstract. Part 1 of this paper has discussed the uncertainties arising from gaps in knowledge or limited understanding of the processes involved in different natural hazard areas. Such deficits may include uncertainties about frequencies, process representations, parameters, present and future boundary conditions, consequences and impacts, and the meaning of observations in evaluating simulation models. These are the epistemic uncertainties that can be difficult to constrain, 20 especially in terms of event or scenario probabilities, even as elicited probabilities rationalised on the basis of expert judgements. This paper reviews the issues raised by trying to quantify the effects of epistemic uncertainties. Such scientific uncertainties might have significant influence on decisions made, say, for risk management, so it is important to examine the sensitivity of such decisions to different feasible sets of assumptions, to communicate the meaning of associated uncertainty estimates and to provide an audit trail for the analysis. A conceptual framework for good practice in dealing with epistemic 25 uncertainties is outlined and implications of applying the principles to natural hazard science are discussed.