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Response to PamW (Reply #25)

Fri Dec 27, 2013, 03:58 PM

26. Classical probability (i), relative-frequency probability (ii), subjective probability (iii)

Classical probability (i), relative-frequency probability (ii), subjective probability (iii)
When independent, university mathematicians compared US nuclear-accident-frequency data, reported from operating experience, with MIT guesses (iii), they discovered that all ‘guesses’ were far too low, by several orders of magnitude. None of the nuclear-accident-frequency data, based on reactor-operating experience, was within the theoretical, 90% confidence interval of the MIT ‘guesses.’Yet there is only a subjective probability of 10% that any of these true (frequency-based) probability values (for different types of reactor accidents) should fall outside this 90% interval. The conclusion? University mathematicians said that MIT assessors were guilty of a massive ‘overconfidence’ bias toward nuclear safety, a typical flaw in most industry-government-funded, nuclear-risk analyses (Cooke, 1982).



...typical atomic-energy advocates use (iii) not (ii) to assess core-melt probabilities, such as when the Nuclear Regulatory Commission (NRC) said core-melt accidents, for all 104 US reactors, would only occur once every 1000 years. Instead, the NRC should have made predictions based on government inspections, independent analyses, and accident-frequency data, not ‘on [subjective-probability] data submitted by plant owners’ (Broder et al., 2011, p. D1). The NRC predecessor agency, the Atomic Energy Commission (AEC) also has a long history of making BSC based on (iii). AEC said the probability of a US nuclear core meltdown is 1 in 17,000 per reactor year (AEC, 1957; Mulvihill et al., 1965).

Even universities erroneously use subjective probabilities (iii), not frequencies (ii), to assess nuclear-core-melt likelihood, particularly when pro-nuclear-government agencies fund their studies. For instance, although the classic, Massachusetts Institute of Technology (MIT)-authored, government-funded, reactor-safety study had frequency data for various nuclear accidents that already had occurred after decades of US-operating experience, it did not use them; instead the MIT authors usedsubjective, pro-nuclear assumptions and conjectures about these accident probabilities (Rasmussen, 1975). When independent, university mathematicians compared US nuclear-accident-frequency data, reported from operating experience, with MIT guesses (iii), they discovered that all ‘guesses’ were far too low, by several orders of magnitude. None of the nuclear-accident-frequency data, based on reactor-operating experience, was within the theoretical, 90% confidence interval of the MIT ‘guesses.’Yet there is only a subjective probability of 10% that any of these true (frequency-based) probability values (for different types of reactor accidents) should fall outside this 90% interval. The conclusion? University mathematicians said that MIT assessors were guilty of a massive ‘overconfidence’ bias toward nuclear safety, a typical flaw in most industry-government-funded, nuclear-risk analyses (Cooke, 1982).




The Frequency Fallacy

A second illegitimate defense of BSC is through the frequency fallacy, confusing core-melt-relative-frequency data with subjective probabilities. Yet ‘probability’ can mean: (i) ‘classical probability;’ (ii) ‘relative frequency;’ or (iii) ‘subjective probability,’ not all of which are applicable to nuclear-core-melt assessment.

Classical probability (i) is illustrated by card games in which the deck contains a fixed number of cards, for example 52. The probability of an event (e) thus equals the number of possible favorable outcomes (f) divided by the total number of possible outcomes (n): P(e) = f/n. Provided the deck of cards is fair, each card has an equal chance of being picked, and the probability (i) of picking an ace = 4/52. Thus, (i) assumes that all possible outcomes are equally likely and that we know n—neither of which is the case regarding nuclear-accident outcomes.

Relative-frequency probability (ii) is often used for cases where the number of outcomes (n) is so great that all typically cannot be observed, as in the probability (ii) that current 5-year-olds will contract cancer. We cannot observe all 5-year-olds throughout their lifetimes, but can reliably predict cancer probability for random, typical 5-year-olds, if we observe a large-enough, long-enough sample. Thus, if we observed 1000 5-year-olds over their lifetimes, if samples were representative and large enough, and if we observed 350 cancer deaths, we could say this cancer probability was roughly P(e) = 35.0% (350/1000). We cannot predict with certainty, however, unless we know the frequency of all relevant events—whether lifetime cancers or total nuclear-core melts. Given that preceding core-melt lists include all occurrences (consistent with the three caveats), those lists suggest an almost-certain, core-melt probability (ii) = core melts/total reactors = 26/442 = roughly a 6% probability (ii)—roughly a 1 in 16 chance of core melt—which is hardly a low probability.

Subjective probability (iii) relies only on what people think particular probabilities are. The odds people get when they bet at racetracks are subjective probabilities because if the probabilities were objective, smart players would always win. Obviously (iii) does not provide reliable nuclear-core-melt probabilities because it is based not on facts, but on what people think about facts. Nuclear proponents think the facts are one way, and opponents think they are another. Both cannot always be correct. Since (iii) is subjective and could be inconsistent, and because (i) would require knowing n and knowing a falsehood (that all reactor outcomes were equally likely), (ii) appears most relevant to nuclear-core-melt assessment.

As preceding sections revealed, however, typical atomic-energy advocates use (iii) not (ii) to assess core-melt probabilities, such as when the Nuclear Regulatory Commission (NRC) said core-melt accidents, for all 104 US reactors, would only occur once every 1000 years. Instead, the NRC should have made predictions based on government inspections, independent analyses, and accident-frequency data, not ‘on [subjective-probability] data submitted by plant owners’ (Broder et al., 2011, p. D1). The NRC predecessor agency, the Atomic Energy Commission (AEC) also has a long history of making BSC based on (iii). AEC said the probability of a US nuclear core meltdown is 1 in 17,000 per reactor year (AEC, 1957; Mulvihill et al., 1965).

Even universities erroneously use subjective probabilities (iii), not frequencies (ii), to assess nuclear-core-melt likelihood, particularly when pro-nuclear-government agencies fund their studies. For instance, although the classic, Massachusetts Institute of Technology (MIT)-authored, government-funded, reactor-safety study had frequency data for various nuclear accidents that already had occurred after decades of US-operating experience, it did not use them; instead the MIT authors used subjective, pro-nuclear assumptions and conjectures about these accident probabilities (Rasmussen, 1975). When independent, university mathematicians compared US nuclear-accident-frequency data, reported from operating experience, with MIT guesses (iii), they discovered that all ‘guesses’ were far too low, by several orders of magnitude. None of the nuclear-accident-frequency data, based on reactor-operating experience, was within the theoretical, 90% confidence interval of the MIT ‘guesses.’Yet there is only a subjective probability of 10% that any of these true (frequency-based) probability values (for different types of reactor accidents) should fall outside this 90% interval. The conclusion? University mathematicians said that MIT assessors were guilty of a massive ‘overconfidence’ bias toward nuclear safety, a typical flaw in most industry-government-funded, nuclear-risk analyses (Cooke, 1982).

This fallacious substitution of subjective probabilities (iii)—for nuclear-core-melt frequencies (ii)—has at least two interesting parallels, namely, nuclear-industry preferences for subjective opinions, over empirical data, in reporting both nuclear costs and carbon-equivalent emissions. Since most nuclear-industry-performed studies employ purely subjective economic estimates, instead of empirical-cost data, they counterfactually assume that nuclear-load factors are 90–95%, that average reactor lifetimes are 50–60 years, and that nuclear-construction-loan-interest rates are 0%. Yet in reality, industry-collected empirical data show average nuclear-load factors are 71%, not 90–95%; average reactor lifetimes are 22, not 50–60 years; and nuclear-interest rates are at least 15%, not 0%. When one corrects only five subjective (counterfactual) nuclear-cost assumptions with actual empirical data, nuclear costs rise 700% above industry-reported costs, revealing that fission is far more expensive than wind or solar-photovoltaic. Similarly, most nuclear-industry-performed studies claim that atomic energy is carbon-emissions-free—a claim dependent on subjectively counting only emissions from reactor operation, not emissions from the entire, 14-stage nuclear-fuel cycle. Once one counts all fuel-cycle emissions, the ratios of carbon emissions are roughly 112 coal : 49 gas : 7 nuclear : 4 solar : 1 wind. For low-grade-uranium ores, the nuclear ratios are even worse: 112 coal : 49 gas : 49 nuclear : 4 solar : 1 wind (Shrader-Frechette, 2011).


From the journal
Ethics, Policy & Environment

Fukushima, Flawed Epistemology, and Black-Swan Events
Dr Kristin Shrader-Frechette

The full discussion is available for download here
http://www.tandfonline.com/doi/full/10.1080/21550085.2011.605851

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