Varying correlation coefficients can underestimate uncertainty in probabilistic models

In accounting for the dependencies among variables in probabilistic (convolution) models, a sensitivity study that varies a correlation between plausible values, even the extremes of +1 and -1, cannot characterize the possible range of results that could be entailed by nonlinear dependencies. Because a functional modeling strategy that seeks to model mechanistically the underlying sources of the dependencies will often be untenable, a phenomenological approach will often be needed to handle dependencies. We summarize recent algorithmic advances that allow the calculation of results under particular bivariate dependence functions, under only partially specified dependence functions, or even without any assumption whatever about dependence.