Department of Homeland Security Bioterrorism Risk Assessment A Call for Change (2008) / Chapter Skim
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Appendix C: Computational Example Illustrating the Replacement of a Joint Distribution of Arc Probabilities with Marginal Expected Values of Individual Arc Probabilities
Appendix C: Computational Example Illustrating the Replacement of a Joint Distribution of Arc Probabilities with Marginal Expected Values of Individual Arc Probabilities
Pages 80-84
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From page 80... ...
Professor Emeritus, Department of Industrial and Operations Engineering University of Michigan, Ann Arbor, Michigan This appendix illustrates two suggestions from Chapter 3 with illustrative R code. In particular, we consider: • the addition of an 18th stage to represent distributions of alternate consequences; and • replacing distributions of arc probabilities by expected values of the probabilities.
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From page 81... ...
, each with two outcomes. For this example, each path through the tree represents a unique scenario with its own consequence distribution.
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From page 82... ...
The line with circles is the estimate from the methodology employed in the BTRA of 2006, which can also produce risk curves. The line with triangles is the estimate from a greatly simplified algorithm that uses only the marginal expected values of individual arc probabilities and simulations from the consequence distributions.
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From page 83... ...
However, no analysis in the BTRA of 2006 and no improvement in analysis recommended by the committee can make meaningful use of the information available in the family of risk curves, beyond that provided by their expectation. Further, given the improvements proposed for the BTRA to incorporate additional consequence measures and utility functions, the committee does not see upcoming analyses that require the family of risk curves.
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From page 84... ...
The estimated risk distribution from this approach is given as the line with triangles in Figure C.2. If the conditional consequence distributions are given in parametric form, or in numerical look-up tables, calcula tion of the risk distribution can be done exactly, without resorting to estimating these distributions from the outputs of Monte Carlo simulations.
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