Bayesian clinical trial methods sometimes use a conjugate exponential-inverse gamma model for event times. Random inequalities between posterior inverse gamma distributions are used to determine stopping conditions, for example in . Computing these inequalitiy probabilities accounts for nearly all of the computation time used in simulating such trials. This report presents an approximation that could reduce this time by two orders of magnitude.
Cook, John D., "Fast Approximation of Inverse Gamma Inequalities" (October 2012). UT MD Anderson Cancer Center Department of Biostatistics Working Paper Series. Working Paper 77.