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.

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.

Abstract: When storing the results of a very large number of stochastic simulation trials of rare events, the amount of data involved may be prohibitive. Sparse and Non-Congruent Stochastic Roll-up are methods for decomposing and storing the results from Monte Carlo simulations such that the data stored only reflects the trials on which a risk event occurred, or focuses attention on some trials over other trials. When the need arises to view or calculate with the fully expressed data set, the results may be aggregated while maintaining statistical relationships between the components of the simulation.

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.

Abstract: When storing the results of a very large number of stochastic simulation trials of rare events, the amount of data involved may be prohibitive. Sparse and Non-Congruent Stochastic Roll-up are methods for decomposing and storing the results from Monte Carlo simulations such that the data stored only reflects the trials on which a risk event occurred, or focuses attention on some trials over other trials. When the need arises to view or calculate with the fully expressed data set, the results may be aggregated while maintaining statistical relationships between the components of the simulation.