Space Shuttle loss-of-vehicle-and-crew risk
Diablo Canyon
2008 financial debacle
Kansai International Airport
Vioxx
Landing on Mars (Balch)
Google flu predictions
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Predictive failures are more common in probabilistic modeling and simulation than they should be. For instance, NASA estimated the risk of catastrophic failure of the Shuttle to be 1/10,000 per flight, but its observed failure rate was about 1 per 70 flights (Hamlin et al. 2011). The National Weather Service and the Army Corps of Engineers strongly underestimate risks of “100-year floods” and miscommunicate uncertainties about flooding risks (Morss and Wahl 2007; NRC 2006; NWS 1998). Observed failures and near-misses found at the Diablo Canyon Nuclear Power Plant reveal gross understatement of its assessed risks (Lochbaum 2011). Failure cascades in electricity distribution systems are much more common than they are forecasted to be (RAWG 2005; USCPSOTF 2006). Probabilistic assessments understating risks in the financial industry precipitated the 2008 recession (Savage 2012).
These are not random rare events in a discipline that estimates and controls risks well overall. They are not the unlucky but expected tail events sometimes called “noble failures”. They seem instead to be the result of pervasive and systemic errors that undermine the credibility of all modeling and simulation efforts. The comment by a prominent engineer that the 2007 bridge collapse in Minneapolis was a “billion to one” event typifies the raw fact that uncertainties are sometimes not well understood in engineering.
With the rise of advanced graphics and high-performance computing, modeling and simulation in engineering have become beautiful as a result of impressive and sometimes dazzling visualizations, but this has largely been a triumph of style over substance, of format over content. If the predictions miss things that can happen, or seriously underestimate their chances of happening, the models are really only Potemkin Villages of proper analyses. They fail to show us just how bad things could be, and thus we are unprepared when exigencies arise. Even worse, they offer a pretense of serious analysis where there is none, which precludes expenditures of effort that would otherwise be recognized as useful.
These predictive failures are intolerable when the stakes involved in analytical simulations are large. What can be done about this situation? The research solicitation topic identifies a source of this problem as the complexity of the models, and our consequent inability to compute enough samples to reasonably describe the breadth of possible outcomes. This is no doubt a persistent problem, but there are other reasons for the predictive failures. We believe that a pervasive cause of these predictive failures is using analytic methods without the empirical information that they require. The solution to these other causes also solves the problem of too few replications because it sidesteps the use of cumbersome sampling methods altogether. Our proposed approach is to characterize uncertainty about model inputs as collections of probability distribution functions. These collections of distributions are known in the theory of imprecise probabilities as credal sets (Walley 1991). In robust Bayesian analyses (often called Bayesian sensitivity analysis), these sets of posterior or posterior predictive distributions are sometimes called distribution bands (Berger 1994; Basu and DasGupta 1995). Frequentist analyses call them meta-distributions or second-order distributions (Vose 2008).
There are twin myths in modeling and simulation that inhibit benefits from the broader application of uncertainty quantification and analysis. The first myth is that the results of calculations are reliable and precise merely because they are expressed with 7 or 14 decimal places. It is unlikely that many analysts actually believe this myth, but they behave as though they do. Few modelers construct comprehensive uncertainty or sensitivity analyses that might explore the full implications of the limits of knowledge about model structure and parameter values. Without such analyses, we cannot really say whether or to what extent our model outputs should be trusted. The second myth is that a full proper accounting of the uncertainty inherent in the simulations and models would “blow up” to a vacuous conclusion that says nothing because any signal would be lost in the noise of uncertainty. Many people actually seem to believe this pernicious myth which we will show to be as misguided as the first myth, albeit in the opposite direction. What is needed are software tools that automatically undertake comprehensive sensitivity and uncertainty analyses whenever models are executed and do it correctly without falling into either trap of either myth.
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