Model uncertainty in risk analysis

How can we project uncertainty about model variable(s) X through a function f to characterize the uncertainty about Y = f (X) when f itself has not been precisely characterized? Although the general problem of how to quantitatively express and project model uncertainty though mathematical calculations in a risk analysis can be addressed by only a few strategies, all of which seem either dubious or quite crude, there are a variety of special cases where methods to handle model uncertainty are rather well developed and available solutions are both comprehensive and subtle. For instance, uncertainty about the shapes of probability distributions can be captured as credal sets or p-boxes. Likewise, uncertainty about the stochastic dependencies between distributions can be projected using Kolmogorov–Fréchet bounding. Numerical experiments suggest that there is also another special case of model uncertainty that can be addressed fairly robustly: when evidence of the statistical relationship between variables has been condensed into regression analyses. In this case, simple computational strategies can be employed to obtain conservative bounds on Y.