Are we more uncertain with mean 10 or with mean 100? JPL Technical Report Server Ignorance vs. variability: considerations for uncertainty quantification analyses Calculating prediction interval generally includes more assumptions about the distribution of values than a simple standard deviation, no? Brittany Fong has a great post about disaggregated data, as well as Steve Wexler’s post on Jitter Plots. https://www.schwab.com/resource-center/insights/content/choiceology-season-5-episode-1. Another data set of 12, 32, 43, 48, 64, 71, 83 and 87. Terminology: Variation, Variability, Uncertainty. Bratvold, R. B., & Begg, S. H. (2010). It’s like saying ‘her pen’ and ‘her writing device’. Their representation in all available reanalysis products is assessed. Refers to the inherent heterogeneity or diversity of data in an assessment. Uncertainty. to consider uncertainty and variability in assessments. a) what is the probability that we make the better choice? For Stan, that means working on better adaptation. Uncertainty is the component of a reported value that characterizes the range of values within which the true value is asserted to lie. For discrete variables, the high variability, and you’d conclude that the probability that someone is better off after that interaction is >50%, but not that much greater, until you learn that I gave everyone $5. Begg, S., Bratvold, R., & Campbell, J. Variability Uncertainty Quantification Workshop for Joint GN&C and L&D Face-to-Face @ MSFC Erik S. Bailey, EDL GNC Systems Group, Jet Propulsion Laboratory, California Institute of Technology Lee Peterson, Mechanical Division Staff, Jet Propulsion Laboratory, California Institute of … Uncertainty is quantified by a probability distribution which depends upon our state of information about the likelihood of what the single, true value of the uncertain quantity is. Welsh, M. B., Begg, S. H., & Bratvold, R. B. How does this choice impact readers’ beliefs about the size of treatment effects? They’re not exactly the same context, but their overlap/similarity/synonymity (is that a word?) But I do not see the distinction as descriptive versus inferential. Generate alternative system-level designs and subsystem concepts. Are they the same? Uncertainty vs. You should not add standard deviations. But we can also talk about the uncertainty in the age of the next person picked at random from a population. Part of this is wording—there’s an idea that these two words are roughly synonyms—but I think part of it is that most people don’t think of these as being two different ideas. Likewise, it is important for modelers to know if they are building models of variability or uncertainty, and their relationship, if any. Uncertainty quantification (UQ) is the science of quantitative characterization and reduction of uncertainties in both computational and real world applications. The value of flexibility in managing uncertainty in oil and gas investments. This article is published with open access at Springerlink.com Abstract Uncertainty in future climate change presents a key challenge for adaptation planning. Vick, S. G. (2002). This is a good example of what Kyle says above “uncertainty of what?”. How to Calculate. And yes, confidence intervals for the sample mean can be made vanishingly small, while the corresponding prediction intervals for a single outcome, or the tolerance interval for proportion of outcomes remain large. The effect of CO2 varies depending on what is going on with the rest of the Earth/Sun system. Standard Deviation of the Mean vs Standard Deviation. In academic areas outside statistics this befuddlement is a field killer. variability, uncertainty and confidence intervals Jamie Kirkham. Society of Petroleum Engineers. Welsh, M., Rees, N., Ringwood, H. & Begg, S. (2010). Content: Risk Vs Uncertainty Uncertainty arises in partially observable and/or stochastic environments, as well as due to ignorance, indolence, or both. Society of Petroleum Engineers. Quantifying the variability of the annular modes: reanalysis uncertainty vs. sampling uncertainty Edwin P. Gerber1 and Patrick Martineau2 1Courant Institute of Mathematical Sciences, New York University, 251 Mercer Street, New York, NY 10012, USA 2Research Center for Advanced Science and Technology, University of Tokyo, Tokyo, Japan This uncertainty can be categorized in two ways: accuracy and precision. But it’s overkill in that we don’t really need to know the posterior mean to within a twentieth of the posterior standard deviation. Rather than try to pick an early winner, aggressively eliminate alternatives. Society of Petroleum Engineers. It may be better to be explicit than to leave the object implicit in the choice of words (which are to some extent synonymous). An estimate of the Variability between sample means if multiple samples were taken from the same population. The questions the values/graphs are supposed to answer is, But it’s hard to get people off their obsession with lots of iterations to get a really tight estimate of a posterior mean. (3) the actual variation (1/n)(\sum_i(xi – mean)^2) A Best Estimate can only be assessed as best in the context of a probability distribution and the measurements of uncertainty and variability - supported by the data. Kaplan, S. (1997). But it comes up in MCMC and hence in Stan all the time. Variability is quantified by a distribution of frequencies of multiple instances of the quantity, derived from observed data. What does UNCERTAINTY mean? In such cases the uncertainty and variability of BHN may be quite high. We investigate this question in two experiments comparing 95% confidence intervals (means and standard errors) to 95% prediction intervals (means and standard deviations). Recently, Storytelling with Data blogged about visualizing variability. Author. The variability of the estimate of the mean is a measure of uncertainty in the estimate. Uncertianty is quantified by a probability distribution which depends upon our state of information about the likelihood of what the single, true value of the uncertain quantity is. No, really it is the distinction between a measure of variation for the sample mean (which is a function of outcomes), versus the measure of variation for a single outcome. Their representation in all available reanalysis products is assessed. Lindley, D. V. (2013). ASCE Publications. SPE 166269 in SPE Annual Technical Conference and Exhibition. Sorry, accidentally submitted the above on mobile before it was complete. Sources of Variability and Uncertainty. Streamlined approaches that use in vitro experimental data to predict chemical toxicokinetics (TK) are increasingly being used to perform risk-based prioritization based upon dosimetric adjustment of high-throughput screening (HTS) data across thousands of chemicals. For that matter, why on earth do we use such similar terms for such distinct concepts: standard deviation vs. standard error vs. sampling error…sampling distribution vs. sample distribution…I can’t tell you how many times I’ve read that an author computed the sampling error from the sample. The variability of the estimate of the mean is a measure of uncertainty in the estimate. But the variability in the next number produced by my random number generator is typically the same as my uncertainty in the outcome. For example, you can use a measure of relative variation to compare the uncertainty or variation associated with the temperature in two different countries, even if one country uses Fahrenheit temperatures and the other uses Celsius temperatures. I plan a follow-up post diving more into probabilities and uncertainty. The designs that survive are your most robust alternatives. Usually, if one doesn’t understand the difference b/w the descriptive and inferential part of their output, they’ll go with the narrower SEM bars (convenient), missing out on what SEM stands for, compared to SD. Uncertainty analysis must confront the distinction between variability and true uncertainty characterizing possible outcomes. The first experiment finds that participants are willing to pay more for and overestimate the effect of a treatment when shown confidence intervals relative to prediction intervals. A simple example of what to use to express uncertainty, using a medical example: https://www.ncbi.nlm.nih.gov/pmc/articles/PMC3487226/. Thomas, P., Bratvold, R.B. (2013), The Risk of Using Risk Matrices. Jake Hofman, Dan Goldstein, and Jessica Hullman write: Scientists presenting experimental results often choose to display either inferential uncertainty (e.g., uncertainty in the estimate of a population mean) or outcome uncertainty (e.g., variation of outcomes around that mean). Now to explain how variability and volatility differ from uncertainty I will approach it from a couple of different angles. To use in follow-up calculations. I’ve always thought these two concepts were conceptually distinct (we can speak of uncertainty in the estimate of a population average, or variation across the population), but then I started quizzing students, and I learned that, to them, “uncertainty” and ‘variation” were not distinct concepts. —Allen C. Ward Principle #3 – Assume variability; preserve options Solution development is an inherently uncertain process. It does not decrease as you get more data. Describing something as a “risk” is a convenient way of describing an unknown state that mayoccur in the future (and, consequently, may not). Variability is quantified by a distribution of frequencies of multiple instances of the quantity, derived from observed data. Consequently, uncertainty in annular mode variability, e.g., the coupling between the stratosphere and troposphere and the variation in the amplitude and timescale of jet variations throughout the annual cycle, is dominated by sampling uncertainty. Ignorance vs. Also see aleatory vs. epistemic uncertainty. Sometimes these are numerically similar, often they’re not. uncertainty is modelled by alternative probability density functions. Comprehensive assessments also involve treatment of the variability and uncertainty associated with those data. The standard deviation of the mean estimates the variability between samples whereas the standard deviation measures the variability within a single sample. Both subgroup reports give details of references where further informatioay be n and guidance m obtained. Therefore, the general lesson of this study is that internal variability should be analysed in order to properly distinguish the impact of other sources of uncertainty, especially for short‐term sensitivity simulations. Streamlined approaches that use in vitro experimental data to predict chemical toxicokinetics (TK) are increasingly being used to perform risk-based prioritization based upon dosimetric adjustment of high-throughput screening (HTS) data across thousands of chemicals. I guess a better description of the distinction (or lack thereof) is that people confuse ‘x is better than y, on average’ with ‘x will be better than y in this case specifically’ when really we should care about both. Variability refers to real differences over time, space, or members of a population and is a property of the system being modeled (e.g., inhalation rates of individuals living in a specific location as a function of their different activity levels). > Sometimes I try to make this point by distinguishing between uncertainty and variation. Lines aren’t the only choice, but they are conventional. It is based on the work of the NDAWG Uncertainty and Variability subgroup which was reported in two NDAWG reports [Refs 1, 2]. & Bickel, J.E. It is evident that sources of uncertainty and variability exist in the following areas: ISO standards, supplementary guides, software tools, life cycle inventory (LCI) databases, all four methodological phases of LCA, and use of LCA information. In essence, Frequentism starts with the diktat that many of these are identical always and forever. Making good decisions. if I’m graphing how much money people on the streets have in their wallet before and after I interact with them, you could get a graph similar to your blog post illustration, i.e. The point of that post was that the biggest example of this confusion is the climate sensitivity. It could be super misleading if values are correlated, i.e. Conversely, uncertainty refers to a condition where you are not sure about the future outcomes. Finance/trading struggles with this as well. Risk, uncertainty and profit. Uncertainty, Variability, Randomness, and Manufacturing Systems Engineering Previous Research 1. Quantifying the variability of the annular modes: reanalysis uncertainty vs. sampling uncertainty Edwin P. Gerber1 and Patrick Martineau2 1Courant Institute of Mathematical Sciences, New York University, 251 Mercer Street, New York, NY 10012, USA 2Research Center for Advanced Science and Technology, University of Tokyo, Tokyo, Japan Statistics. And that would be clear from an error graph: that it’s a small, but certain improvement. Variability: What's the Difference and Why is it Important? In addition, there is epistemic uncertainty in parameters that are not random by have only a single correct (but unknown) value. Basically, the climate sensitivity to CO2 is not a constant. SIAM review, 49(2), 211–235. The efficient frontier I care about is wall time to effective sample size 100 or even 50 vs. power usage (to adjust more multiple cores, GPUs, etc.) Winterfeldt (Editors), Advances in Decision Analysis. Uncertainty and variability are properties of (abstract) objects, that may or may not intersect depending on which objects are being referred to and the specific context. (error) We use the terms risk and uncertainty in a single breath, but have you ever wondered about their difference. Sometimes I try to make this point by distinguishing between uncertainty and variation. Uncertainty can be either due to variability or due to lack of knowledge. Now to explain how variability and volatility differ from uncertainty I will approach it from a couple of different angles. . (posterior distribution of the parameters), 3) At the next level, what can we numerically calculate from the posterior (MCMC standard errors). I mean, just look at the graphs – why on earth do we as statisticians have the convention where the same “error bar” formulation is used to display both completely different quantities? As nouns the difference between variability and uncertainty is that variability is the state or characteristic of being variable while uncertainty is (uncountable) doubt; the condition of … The second experiment evaluates how alternative visualizations compare to standard visualizations for different effect sizes. In other words, the range of values for climate sensitivity is a derived property of the data (plus assuming a linear relationship between temp and forcing). 2. For many types of risk assessments, it is important to clearly distinguish between uncertainty and variability (see Hoffman and Hammonds reference in the Bibliography). New York: Hart, Schaffner and Marx. In SPE Annual Technical Conference and Exhibition. One of the issues inuncertainty analysis that must be confronted is how to distinguish between the relativecontribution of variability (i.e., heterogeneity) and true uncertainty to the characterization ofpredicted population risk. Which leads us to the question: What does the mean mean? 1 This chapter addresses how, in the context of waste incineration, uncertainty and variability are defined, characterized, and treated in the risk-assessment and riskcommunication process. I’m talking about uncertainty vs. variation. The Foundations of Decision Analysis Revisited. (2007). These results make sense. Conversely, uncertainty refers to a condition where you are not sure about the future outcomes. I argued that, had the graph not been there, I would’ve wanted to see the data. Howard, R.A., 2007. https://bayes.wustl.edu/etj/articles/stand.on.entropy.pdf, https://www.epa.gov/expobox/uncertainty-and-variability, 17 state attorney generals, 100 congressmembers, and the Association for Psychological Science walk into a bar. variability Clara Deser • Adam Phillips • Vincent Bourdette • Haiyan Teng Received: 30 July 2010/Accepted: 18 December 2010/Published online: 31 December 2010 The Author(s) 2010. They change with each re-calculation. Therefore, the general lesson of this study is that internal variability should be analysed in order to properly distinguish the impact of other sources of uncertainty, … 1) At the highest level, which model should we use? The variability of the time when I look at the clock is generally larger than the uncertainty in that time. This paper thus provides a resource for technical professionals and teachers to clarify the distinction between the two, or to correct it where it has been wrongly taught, and thereby help to improve decision-making. Diaconis, P., Holmes, S., & Montgomery, R. (2007). https://statmodeling.stat.columbia.edu/2020/05/09/standard-deviation-standard-error-whatever/, > we can speak of uncertainty in the estimate of a population average, or variation across the population. Then there’s several distinct entities: (1) the Uncertainty around each xi computed from the marginal distributions P(xi) Bratvold, R.B. We discuss and clarify the distinction between uncertainty and variability through strict definition, illustrative analogy and numerical examples. Society of Petroleum Engineers. variability, it is important to differentiate between parameter estimate uncertainty, model parameterization effects, and actual spatial variability. We show there is no objectively ‘right’ probability distribution for quantifying the uncertainty of an unknown event – it can only be ‘right’ in that it is consistent with the assessor's information. Variability. For example, such a distinction is required for quantitative characterization of uncertainty in population risk or in individual risk. Variability is quantified by a distribution of frequencies of multiple instances of the quantity, derived from observed data. Coronavirus Grab Bag: deaths vs qalys, safety vs safety theater, ‘all in this together’, and more. Risk analysis, 17(4), 407–417. Uncertainty and variability are properties of (abstract) objects, that may or may not intersect depending on which objects are being referred to and the specific context. is consolidated and reviewed. Daniel Kahneman talks here about the distinction/confusion among noise, biases, and variance. Our experience as educators of students and oil & gas industry personnel suggests that significant confusion exists in their understanding of the distinction between variability and uncertainty. Combining model uncertainty and uncertainty because of interannual variability Components of uncertainty For understanding the solar radiation model performance key indicators, it is important to consider the several factors that influence on the accuracy of the values, provided both by satellite-based modelling and on-site ground sensors. Flow Line Analysis M 1 B M 2 Five cases of two-machine lines: N P 0.78 0.8 0.82 0.84 0.86 0.88 0.9 0.92 0 20 40 60 80 100 120 140 160 180 200 Production rate vs … Well, I don’t know: are they referring to the same ‘her’, who is she, and how does she like to do her writing? The biggest example of this confusion is all the people trying to decrease the uncertainty in the climate sensitivity. Knight, F. H. (1921). Notice that these estimates are variable. Yes, standard deviation is descriptive. He doesn’t say anything particularly profound…but you might find it worth listening to in terms clarifying these concepts with students. which uncertainty and variability have been incorporated into IRIS assessments. Uncertainty is quantified by a probability distribution which depends upon our state of information about the likelihood of what the single, true value of the uncertain quantity is. Theyve been publishing papers about this for fecades. I’m also a fan of Nathan Yau’s Flowing Data post about visualizing uncertainty. This variability is measured by a standard deviation. SPE Hydrocarbon Economics and Evaluation Symposium (19 May 2014 - 20 May 2014 : Houston, Texas) Published. And if lots of students don’t get this distinction, it’s no surprise that researchers and consumers of research also get stuck on this. The U.S. Department of Energy's Office of Scientific and Technical Information Uncertainty is quantified by a probability distribution which depends upon our state of information about the likelihood of what the single, true value of the uncertain quantity is. I feel that the blog illustration is misleading because the deviation bars are so long and have the same thickness throughout, they’ll intuitively look like linear distributions and not normals if you’re not trained. Quantifying the variability of the annular modes: Reanalysis uncertainty vs. sampling uncertainty Edwin P. Gerber1 and Patrick Martineau2 1Courant Institute of Mathematical Sciences, New York University, 251 Mercer Street, New York NY 10012, USA 2Research Center for Advanced Science and Technology, University of Tokyo, Japan Correspondence: Edwin P. Gerber (firstname.lastname@example.org) Three separate MC simulations were performed: variability only, uncertainty only, and both uncertainty and variability. Welsh, M. B., Bratvold, R. B., & Begg, S. H. (2005). The fact that it is a small improvement needs to be concluded from my knowledge of the domain and the actual values. This design scenario is known as an “a priori” analysis associated with reliability-based design, and forms the basis of design standards for buildings in the United States, Canada, Europe, Australia and elsewhere [ 39 ]. This project is based on work that was developed during Dettmer’s PhD and postdoctoral research. Error bars are fairly universally based on a Gaussian distribution, not a uniform one. In other words, uncertainty in science refers to the idea that all data have a range of expected values as opposed to a precise point value. It is not supposed to get more precise any more than standard deviation is supposed to approach zero as you collect more data. Variability refers to quantities that aredistributed within a defined population, such as: food consumption rates,exposure duration, and expected lifetime. It may be better to be explicit than to leave the object implicit in the choice of words (which are to some extent synonymous)”. If something will occur (e.g., the setting of the sun), there is no uncertainty and therefore no “risk.” The mathematical pro… The priors are supposed to be used on f and sigma_f, not on climate sensitivity. Adding more MCMC draws reduces the MCMC standard error, but the posterior standard deviation doesn’t change. In your example, you’d presumably (or at least you should) use a paired design rather than treating the ‘before’ and ‘after’ as two samples (at which point all your differences would lie exactly at $5, so you’d have a standard deviation of 0 anyway). Scientific uncertainty is a quantitative measurement of variability in the data. Combining model uncertainty and uncertainty because of interannual variability Components of uncertainty For understanding the solar radiation model performance key indicators, it is important to consider the several factors that influence on the accuracy of the values, provided both by satellite-based modelling and on-site ground sensors. is contextual. In other words, uncertainty in science refers to the idea that all data have a range of expected values as opposed to a precise point value. Descriptive Statistics • Describe the characteristics of a sample • Graphical methods – E.g. The systematic effect over 1 year shows distinct patterns for the multi‐physics and the internal variability. (4) the estimate of the variation E((1/n)(\sum_i(xi – mean)^2)] Uncertainty: a Guide to dealing with uncertainty in quantitative risk and policy analysis Cambridge University Press. New York, New York, USA. There, of course, is a third frequentist interval commonly used, the tolerance for a proportion of the outcomes in the population (or equivalently a prediction interval for any number of future outcomes. But uncertainty in science does not imply doubt as it does in everyday use. Any suggestions? Are we more uncertain with mean 10 or with mean 100? I’m reminded of the example from a few months ago where someone published a paper including graphs that revealed the sensitivity of its headline conclusions on some implausible assumptions. In statistics, propagation of uncertainty (or propagation of error) is the effect of variables' uncertainties (or errors, more specifically random errors) on the uncertainty of a function based on them. Problems with the elicitation of uncertainty. Equation. The remainder of Section 1 presents an introduction to this topic, a description of the purpose and focus of the study, and background information to provide historical perspective on how uncertainty and variability have been addressed in the IRIS program. Well, this article might help you in understanding the difference between risk and uncertainty, take a read. Scientific uncertainty is a quantitative measurement of variability in the data. In: W. Edwards, J. RalphF. But a lot of people would just accept the estimate and standard error and not want to know more. That both are represented by ‘distributions’ is a major source of confusion, which can lead to uncritical adoption of frequency distributions to represent uncertainty, and thus to erroneous risk assessments and bad decisions. Sources of uncertainty in rock slope engineering Parameter uncertainty What are these telling us? (5) the uncertainty of the estimate of the variation. (2) the Uncertainty around the entire sequence x1,…,xn which is something like the entropy computed from P(x1,…,xn) Morgan, M. G., & Henrion, M. (1990). 5 Aleatory Variability and Epistemic Uncertainty Aleatory variability and epistemic uncertainty are terms used in seismic hazard analysis that are not commonly used in other fields, but the concepts are well known. APPEA Journal, 50(1), pp 389–401. 32–56. Thus, different people (or teams or companies) can legitimately hold different probabilities for the same event. If you didn’t, then sure, you might miss the evidence. The annular modes characterize the dominant variability of the extratropical circulation in each hemisphere, quantifying vacillations in the position of the tropospheric jet streams and the strength of the stratospheric polar vortices. Dynamical bias in the coin toss. Variability is one cause of uncertainty, the conﬁdence or precision with which a quantity can be assigned a value. How variable is mean 10 compared to mean 100? It is important that they distinguish whether they are being asked for variability ranges or uncertainty ranges. . The question then arose: what if the paper had not included the graph, then maybe no one would’ve realized the problem. The above example should make it clear that if the data points are values of the same parameter in various experiments, then the first data set is a good fit, but the second one is too uncertain. Look around page 64 under “fluctuations”. One of the things I have been thinking about is expanding on the meaning of probability into what would repeatedly happen in a chosen fake world that hopefully is like ours. Uncertainty means we do not know the value (or outcome) of some quantity, eg the average porosity of a specific reservoir (or the porosity of a core-sized piece of rock at some point within the reservoir). b) what is the probability that the better choice leads to a better individual outcome? I suspect whether one identifies these concepts as separate may depend on the specific examples one is thinking of when asked about it, which is probably highly dependent on the person’s own context. Notice that these estimates are variable. The reason to calculate a percentage uncertainty is: 1. Society of Petroleum Engineers. This variability is measured by a standard deviation. How variable is mean 10 compared to mean 100? MCMC standard error on the estimate of a posterior mean for a quantity is the posterior standard deviation of that quantity divided by the square root of the effective sample size. Frequentism is naturally going to make people equate uncertainty with variation, which is a recipe for endless befuddlment especially since the uncertainty *is* sometimes numerically similar to the variation. They want open peer review for their paper, and they want it now. To get a sense how accurate the measurement is. In this paper, the effects of using each approach to account for V s uncertainty in site response are investigated by linking the dispersion misfit values for each V s profile to variability in equivalent linear site response estimates. And Manufacturing Systems engineering Previous research 1 data blogged about visualizing uncertainty than deviation! Re not exactly the same as my uncertainty in the quantity, derived observed! Answer is, a ) what is the probability that the better-looking choice to! And numerical examples [ 1 ]: “ the question is “ uncertainty about means, innit in risk. Where further informatioay be n and guidance m obtained talks here about the distribution of values than a simple of! See the distinction between variability and volatility differ from uncertainty I will approach from! 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