What Monte Carlo methods cannot do

Although extremely flexible and obviously useful for many risk assessment problems, Monte Carlo methods have four significant limitations that risk analysts should keep in mind. (1) Like most methods based on probability theory, Monte Carlo methods are data-intensive. Consequently, they usually cannot produce results unless a considerable body of empirical information has been collected, or unless the analyst is willing to make several assumptions in the place of such empirical information. (2) Although appropriate for handling variability and stochasticity, Monte Carlo methods cannot be used to propagate partial ignorance under any frequentist interpretation of probability. (3) Monte Carlo methods cannot be used to conclude that exceedance risks are no larger than a particular level. (4) Finally; Monte Carlo methods cannot be used to effect deconvolutions to solve backcalculation problems such as often arise in remediation planning. This paper reviews a series of 10 exemplar problems in risk analysis for which classical Monte Carlo methods yield incorrect answers.