Over the last decade or so, there have been many developments in methods to handle uncertainty in cost-effectiveness studies. In decision modelling, it is widely accepted that there needs to be an assessment of how sensitive the decision is to uncertainty in parameter values. The rationale for probabilistic sensitivity analysis (PSA) is primarily based on a consideration of the needs of decision makers in assessing the consequences of decision uncertainty. In this paper, we highlight some further compelling reasons for adopting probabilistic methods for decision modelling and sensitivity analysis, and specifically for adopting simulation from a Bayesian posterior distribution. Our reasoning is as follows. Firstly, cost-effectiveness analyses need to be based on all the available evidence, not a selected subset, and the uncertainties in the data need to be propagated through the model in order to provide a correct analysis of the uncertainties in the decision. In many - perhaps most - cases the evidence structure requires a statistical analysis that inevitably induces correlations between parameters. Deterministic sensitivity analysis requires that models are run with parameters fixed at extreme values, but where parameter correlation exists it is not possible to identify sets of parameter values that can be considered extreme in a meaningful sense. However, a correct probabilistic analysis can be readily achieved by Monte Carlo sampling from the joint posterior distribution of parameters. In this paper, we review some evidence structures commonly occurring in decision models, where analyses that correctly reflect the uncertainty in the data induce correlations between parameters. Frequently, this is because the evidence base includes information on functions of several parameters. It follows that, if health technology assessments are to be based on a correct analysis of all available data, then probabilistic methods must be used both for sensitivity analysis and for estimation of expected costs and benefits.