Abstract: A method of efficiently modeling changes to mitigation of an occurrence of a rare event for a number of simulation trials includes obtaining or generating a number of sparse simulation trials of a simulation including a total number of simulation trials (x) associated with the N occurrences of a rare event, assigning fractions of 1/N to N/N to the sparse simulation trials, filtering the sparse simulation trials by the assigned fractions by a percentage corresponding to y/N to simulate a mitigation of the likelihood of failure, and outputting sparse simulation trials that are less than the percentage to statistically represent the effects of the mitigation on the total number of trials.