<<See Uncertain Numbers. This site "Decoder ring" and its several subpages are a proving ground for material that will go to Uncertain Numbers or to a book on this subject.>>
The distinction between the two basic kinds of uncertainty has been discovered many times in various fields. Each time, a slightly different vocabulary is created to discuss these uncertainties and their implications. The secret decoder ring below is a synopsis and guide to references for the various terms that have come into common use in these respective fields. An abbreviated version of the decoder ring based on an early version of this one appeared in Warren-Hicks and Hart (2010, page 2).
We would be interested in your suggestions for additions or amendments to the decoder ring. Please send them to admin @ ramas . com.
Apostolakis, G. 1999. The distinction between aleatory and epistemic uncertainties is important: An example from the inclusion of aging effects into probabilstic safety assessment. Proceedings of the PSA'99, August 22-25, 1999, American Nuclear Society, Washington DC.
Apostolakis, G.E., 1994. A Commentary on model uncertainty. In Proceedings of Workshop I in Advanced Topics in Risk and Reliability Analysis, Model Uncertainty: Its Characterization and Quantification, A. Mosleh, N. Siu, C. Smidts, and C. Lui, Eds.
Casti, J.L. 1990. Searching for Certainty: What Scientists Can Know about the Future. William Morrow, New York.
Hattis, D. D.E. Burmaster. 1994. Assessment of variability and uncertainty distributions for practical risk analyses. Risk Analysis 14: 713–730.
Hoffman, F.O., and J.S. Hammonds. 1994. Propagation of uncertainty in risk assessments: the need to distinguish between uncertainty due to lack of knowledge and uncertainty due to variability. Risk Analysis 14: 707–712.
Ferson, S. and L.R. Ginzburg. 1996. Different methods are needed to propagate ignorance and variability. Reliability Engineering and Systems Safety 54:133–144.
Klir, G.J. and B. Yuan 1995. Fuzzy Sets and Fuzzy Logic: Theory and Applications. Prentice Hall.
Knight, F.H. 1921. Risk, Uncertainty and Profit. Houghton Mifflin, Boston.
Merrick, J.R.W.; Dinesh, V.; Amita Singh; van Dorp, J.R.; Mazzuchi, T.A. 2003. Propagation of uncertainty in a simulation-based maritime risk assessment model utilizing Bayesian simulation techniques. Pages 449 – 455 in Simulation Conference, Proceedings of the 2003 Winter, Volume 1, 7-10 December 2003.
Walley, P. 1991. Statistical Reasoning with Imprecise Probabilities. Chapman and Hall, London.
Warren-Hicks, W.J., and A. Hart (editors) 2010. Application of Uncertainty Analysis to Ecological Risks of Pesticides. SETAC Press, Pensacola, Florida.
Winkler, R.L. 1996. Uncertainty in probabilistic risk assessment. Reliability Engineering and System Safety 54: 127-132.
Notes
Mark Colyvan uses ‘epistemic uncertainty’ in a way that includes both variability and incertitude.
A paper we reviewed for Warner North in his capacity as editor at Risk Analysis used ‘risk’ for both Knightian risk and Knightian uncertainty!
On 11/9/08, William Warren-Hicks < > wrote:
You know, at first glance, I really like the decoder ring table. After I get some sleep and wake up tomorrow (I've been up since 5 working on this book), I will take another look. I think it might make sense to add it to the Introduction to show how the terms are somewhat interchangeable.
Can you provide me some references, to include in the Introduction, for the various rows in the table. I think this would be a big help. I'm not familiar with Walley et al, for example. It would probably serve the reader to show that the terms can be difficult to master, give them additional references, and then we will be home free.
thanks,
-bill
At 08:34 PM 11/9/2008, you wrote:
Bill:
Thanks for calling me about this. I would have hated not getting a chance to help resolve it, which I think is very easy to do. My recommendation is to slightly edit Andy's chapter to correct the inconsistency in minimally invasive way.
1) All we really need to do is change the phrase "in this book" on the first page of chapter 1 to "in this chapter and most of the book". This small change corrects the essential inconsistency that you noticed.
2) I think you or Andy might also want to delete the unnecessary argument consisting of three sentences starting with "In common usage…". You can retain the argument if Andy so desires, but I think it's going to be a little beside the point to almost all readers. (In addition to its being distracting, I think the text is also wrong, as I elaborate below.)
3) Finally, I would replace "the majority of" with "most". This is another example where synonomy does not imply equivalence. The word 'majority' implies that Andy took a vote, but I don't think he did anything like that.
I've implemented these three minor changes on the copy of Andy's chapter that you sent me in Word's track-changes mode. Let me know if you, or Andy, would like to discuss further this or any other matters. I'll be in the office (1-631-751-4350) most every afternoon this week. Except Monday, when I'll be at home (1-631-751-7135).
Below are some further thoughts on this matter. It's trivial, but it can be a source of confusion to neophytes, so I think that questions of nomenclature and basic vocabulary are worth thinking carefully about.
It was startlingly amusing that Andy contradicts his own argument in the very first sentence of section 1.1. He says "uncertainties" have three sources. Ha! Thus, he agrees with me that stochasticity and ignorance both give rise to uncertainties. Moreover—and I think this is the killing rejoinder—throughout the discussion he uses the phrase "uncertainty analysis" to refer to a whole bunch of analyses including ordinary Monte Carlo, two-dimensional Monte Carlo, and even (non-probabilistic) interval analysis. This doesn't make sense unless you're using 'uncertainty' as an umbrella term for both reasons for not-knowing.
The argument that the OED says 'uncertainty' and 'incertitude' are synonyms is hardly a compelling reason not to ascribe technical specializations to the two words if that can be done in a reasonable way. The words 'diction' and 'pronunciation' are (becoming) synonyms too, but we're fine with having both words in use, and with sometimes even drawing distinctions between the two words. The other argument that 'incertitude' means 'uncertainty' in French is also uncompelling. 'Formidable' means 'great' in French too, and yet something else in English, so what? Will French readers suddenly get confused more than they have been?
Andy is certainly wrong that EPA's terminology of 'variability' and 'uncertainty' and no term for their combination is pervasive. In fact, this is the convention for a minority of quantitative analysts (by census, rather than vote). The engineer's use of the modifiers 'aleatory' and 'epistemic' is much more common, and more widely used among government agencies.
Here is a handy decoder ring for you, Bill, among the various terms you might encounter as they are used in different communities:
Community Stochasticity/randomness Ignorance/doubt Combination of both
Scott, Dwayne, et al. variability incertitude uncertainty
EPA (mostly biologists) variability uncertainty variability & uncertainty
Engineers and physicists aleatory uncertainty epistemic uncertainty uncertainty
Bayesian statisticians uncertainty uncertainty uncertainty
Frequentist statisticians uncertainty -- uncertainty
Risk analysts Type I uncertainty Type II uncertainty uncertainty
Systems theorists conflict non-specificity ambiguity
Walley, et al. chance imprecision imprecise probability
These three columns represent three distinct ideas, merely called various things by different people. But a rose by any other name…. If, for your own reasons, you'd like to get a handle on just what that ignorance/doubt column is and why people keep wanting to treat it specially, you might consult <http://www.maths.dur.ac.uk/users/matthias.troffaes/jstpip/improb.html>http://www.maths.dur.ac.uk/users/matthias.troffaes/jstpip/improb.html.
Cheers,
Scott
P.S. The title line of chapter 6 still refers to "8". And, oops, it's got some other serious problems too.
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William Warren-Hicks, Ph.D.
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