The Effect of Neglecting Correlations When Propagating Uncertainty and Estimating the Population Distribution of Risk

Smith, A.D.; Pb, Ryan; Evans, John S.

doi:10.1111/j.1539-6924.1992.tb00703.x

Cited by 104 publications

(51 citation statements)

References 17 publications

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“…The Supporting Information (Table S2) provides further details about the magnitude and uncertainty distributions of these parameters. We have assumed that none of the model inputs are correlated, as asserted in previous studies (14)(15)(16)(17)(18)36).…”

Section: Prior Uncertainty Distributionsmentioning

confidence: 99%

Using Information on Uncertainty to Improve Environmental Fate Modeling: A Case Study on DDT

Schenker

Scheringer

Sohn

et al. 2008

Environ. Sci. Technol.

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Section: Prior Uncertainty Distributionsmentioning

confidence: 99%

Using Information on Uncertainty to Improve Environmental Fate Modeling: A Case Study on DDT

Schenker

Scheringer

Sohn

et al. 2008

Environ. Sci. Technol.

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“…Smith et al (1992) found that ignoring correlation may seriously bias the resulting risk, however, they also conclude that in some circumstances correlation can be ignored, and give a method for assessing how much effect correlation may have on results. Cicumstances in which correlations may be ignored (because they will not substantially impact results) include:…”

Section: Correlation Between Parameter Uncertainty Distributionsmentioning

confidence: 99%

Use of Monte Carlo methods in environmental risk assessments at the INEL: Applications and issues

Harris¹,

Horn²

1996

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Under DOE Idaho Operations Office Contract DE-AC07-941Di3223. I DISCLAIMERPortions of this document may be illegible in electronic image products. Images are produced from the best available original document. Use of Monte Carlo Methods in Environmental Risk Assessment at the INEL:Applications and Issues EXECUTIVE SUMMARYMonte Carlo Analysis (MCA) is a powerful tool for evaluating risks in the presence of uncertainty. The technique could be useful in future environmental risk assessment work done at the Idaho National Engineering Laboratory (INEL). This document provides the background information useful for risk assessors and risk managers to understand MCA. It presents the general methodology of MCA and identifies issues that will need to be resolved before MCA can be effectively implemented at the INEL.MCA is a conceptually simple method of probabilistic risk assessment. For the input parameters in the risk model, a probability distribution is assigned based on available information about the parameter, these distributions are each randomly sampled n times. The n random realizations from each input parameter are then entered into the model to produce n risk estimates. The input distributions take into account uncertainties in those parameters; the resulting risk values provide an estimate of the risk distribution. Hence, the Monte Carlo analysis essentially propagates the input uncertainties through the risk model to the resulting risk estimates.In this report, the motivation for using MCA as an improvement over the baseline risk assessment (BRA) point estimates is given. Two major shortcomings of the point estimate approach is that it suffers from creeping conservatism so that the user does not know how conservative the estimate is, and it provides limited information to the risk manager and public. The use of MCA helps alleviate both of these problems.The use of MCA helps focus attention on the uncertainty in the risk assessment. Further, it provides a quantitative description of the uncertainty. In this way, the manager and stakeholders are better able to understand the risks and are better able to make informed decisions. A key theme of the document is that uncertainty matters and MCA provides a practical description of the uncertainty.V

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“…If a dependency is neglected, the answer obtained by an analysis assuming independence will generally be wrong. Under certain conditions, the central tendency of output distributions could be approximately correct (Smith et al 1992). However, the estimated dispersion and especially the tail probabilities can be highly inaccurate (Bukowski et al 1995;Ferson and Burgman 1995;Ferson 1994).…”

Section: Unjustified Independence Assumptions Harmfulmentioning

confidence: 99%

Dependence in probabilistic modeling, Dempster-Shafer theory, and probability bounds analysis.

Oberkampf¹,

Tucker

Zhang

et al. 2004

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LIBRARY VAULTThis report summarizes methods to incorporate information (or lack of information) about inter-variable dependence into risk assessments that use Dempster-Shafer theory or probability bounds analysis to address epistemic and aleatory uncertainty. The report reviews techniques for simulating correlated variates for a given correlation measure and dependence model, computation of bounds on distribution functions under a specified dependence model, formulation of parametric and empirical dependence models, and bounding approaches that can be used when information about the intervariable dependence is incomplete. The report also reviews several of the most pervasive and dangerous myths among risk analysts about dependence in probabilistic models.*The work described in this report was performed for Sandia National Laboratories under Contract No. 19094. 3 AcknowledgmentsDiscussions with Peter Walley were helpful in elucidating the problem of representing dependence in the context of imprecise probabilities and the role of probability boxes and Dempster-Shafer structures as models of imprecise probabilities. 2.5Using inequalities in risk assessments 2.6Caveat: best-possible calculations are NP-hard 2.7Numerical example: fault tree for a pressure tank Sym b o k -Ea is distributed as is an element of is a subset of plus or minus addition, subtraction, etc. under no assumption about the dependence between the operands addition, subtraction, etc. assuming independence addition, subtraction, etc. assuming perfect dependence addition, subtraction, etc. assuming opposite dependence the empty set, i.e., the set having no members probability-box specified by a left side F(x) and a right side E(x) where E(x) I F ( x ) for all x E %, consisting of all non-decreasing functions F from the reals into [O,l] such that E(x) I F(x) I fix). {(sl,ml),. . ., (s,,m,)} an enumeration of the elements of a Dempster-Shafer structure in terms of its focal elements si and their nonzero masses mi beta (v, w) a beta distribution with shape parameters v and w convolve(X, Y,r) convolution (usually addition) assuming that X and Y have correlation r convolve(X, Y,C) convolution (usually addition) assuming the copula C describes the dependence between X and Y covariance between random variables X and Y expectation (mean) of random variable X a functionfwhose domain is the set A and whose range is the set B. In other words, for any element in A, the functionfassigns a value that is in the set B the step function that is zero for all values of x

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The Effect of Neglecting Correlations When Propagating Uncertainty and Estimating the Population Distribution of Risk

Cited by 104 publications

References 17 publications

Using Information on Uncertainty to Improve Environmental Fate Modeling: A Case Study on DDT

Using Information on Uncertainty to Improve Environmental Fate Modeling: A Case Study on DDT

Use of Monte Carlo methods in environmental risk assessments at the INEL: Applications and issues

Dependence in probabilistic modeling, Dempster-Shafer theory, and probability bounds analysis.

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