Final Report. Support for Risk and Economic Analysis for the National Biodefense Analysis and Countermeasures Center

Transcription

1 Final Report Support for Risk and Economic Analysis for the National Biodefense Analysis and Countermeasures Center Subcontract No. BNBI07009 under Prime Contract HSHQDC-C with the Department of Homeland Security September 30, 2008 Submitted to: Battelle National Biodefense Institute, LLC 110 Thomas Johnson Drive Frederick, MD By: Center for Risk and Economic Analysis of Terrorism Events (CREATE) University of Southern California University Park Los Angeles, CA 90089

2 Table of Contents SUMMARY.iii PROJECT OVERVIEW Summary of Task Summary of Task APPENDIX A Scope of Work and Deliverables Background and Overview Approach Scope of Work Schedule Deliverables...13 APPENDIX B A Framework for Analyzing and Estimating the Total Economic Consequences of Bioterrorist Attacks 1. Introduction General Principles of Loss Estimation Economic Resilience Behavioral and System Linkages Overall Framework Conclusion References...28 APPENDIX C Simulating the Economic Impacts of Various Hypothetical Bio-Terrorist Attacks 1. Introduction Analytical Framework for Case Studies Stadium Attack Scenario Urban Center Attack Scenario Airport Attack Scenario Romaine Lettuce Attack Scenario Conclusion References...69 APPENDIX D Regional Economic Impacts of a Bioterrorist Attack on the Water System of Los Angeles: A Computable General Disequilibrium Analysis Introduction Economic Impacts Characteristics of Water Service Disruptions The Role of Water Services in L.A. County...77 i

3 5. The L.A. CGE Model Water Service Disruption Simulations Broader Implications Conclusion References...96 APPENDIX E Using the Dirichlet Elicitation Tool: A Mini - Tutorial APPENDIX F Using the Dirichlet Aggregation Tool: A Mini - Tutorial APPENDIX G Probabilistic Risk Analysis and Terrorism Risk ii

4 APPENDIX E Using the Dirichlet Elicitation Tool: A Mini-Tutorial Overview By Thomas Eppel University of California at Irvine Irvine, California Overview To facilitate the development of a Dirichlet distribution for a hierarchical partition of events and event groups, the Dirichlet Elicitation Tool (DET) was developed using Microsoft Excel as the main programming tool. This document, in draft form at this time, describes the various sections of the tool and also leads the interested reader through a mini-tutorial about how to use it. From a conceptual perspective, the tool assumes that it is used by an expert in the particular domain for which a Dirichlet distribution is to be constructed. It also assumes a hierarchical partition of the event space. By that, we mean that the user can specify a list of groups for which he or she then will specify individual events. In addition to labeling and describing these groups and events, the user s main task is to specify split-ratios of the likelihood of the events within each group as well as split-ratios of the relative likelihoods among the most likely events from each group. The user also has to provide, in a very interactive manner, a scaling constant k that determines the shape of the marginal beta distributions. Based on these judgments the tool then calculates and reports the event probabilities for the resulting Dirichlet distribution. The programming mainly relies on built-in Excel formulas and functions that dynamically customize the tool and the required judgments depending on user input. A minimal amount of code written in Visual Basic for Applications (VBA is a component of Microsoft Excel) was required to navigate the tool. Since VBA is not part of the Macintosh version of Excel, the DET only runs under the Windows operating system. This draft document describes the individual sections of the DET and provides an example that can be used as a mini-tutorial for exemplary purposes only. Starting the DET It is highly recommended to work with a copy of the DET. Therefore, either make a copy of the file in the Windows Explorer or choose File Save As in Excel. Make sure that you give the file a meaningful name (e.g., name of the expert). Since the DET contains VBA code, you might be asked whether or not you want to enable Macros when you load the file (this depends on the specific configuration of Excel on your computer). Make sure that you enable the Macros

5 Main Menu Figure 1 The Main Menu provides easy access to all of the individual modules of the DET. It consists of the following sections and can be accessed from each of these sections: Define Events: Click on this button to access the section, which allows the user to input the individual events. This section then also allows the user to define ranks, ratios and/or split ratios for the individual events. Define k: Click on this button to access the section, which allows the user to interactively adjust the scaling constant k to adjust the shape of the individual beta distributions. Summary Report: Click on this button to access the section, which allows the user to view and print the calculated results for the Dirichlet distribution based on the user inputs from the other sections

6 The main menu also asks for general project information (date of elicitation, project name, names of facilitator and expert) in the greenly shaded area. For the purpose of this mini-tutorial, fill in the information as shown in Figure 2. NOTE: In general, only use greenly shaded areas to provide input to the DET. Changing any other information can crash the tool or make it unusable. Figure 2-5 -

7 Defining Events Figure 3 In this section, the user defines the individual events (up to 10) and determines their average frequencies. This can be done using ratios, split fractions or a direct distribution of 100 points among the events. For each mode, the DET automatically calculates the corresponding average frequencies. Since the DET does not force any consistencies, the rank order of events between different elicitation modes can differ. The user can re-order the events by clicking on the corresponding Reorder button above a particular elicitation mode (e.g., if you want the events order according to the Ratio judgments, click the Reorder button above the Ratio label). Such a re-ordering - 6 -

8 does not make sense for the split fractions, as these fractions are not necessarily a monotonic function of the ranks. NOTE: if events are re-ordered, any previously elicited split fractions need to be re-elicited, as they should now be defined over a different rank order of events. IMPORTANT: The user MUST decide which of the judgments to use. This can be done by clicking on the corresponding Use button above the average frequencies of the chosen elicitation mode (e.g., click on the Use button above the Avg. Freq. for split fractions if you want to use split fractions). Clicking any Use button will copy the events and their corresponding average frequencies to the range A7:B16 and will also change the bar graph of expected frequencies. The user can also input comments in the Comments section (one line at a time). For the purpose of this mini-tutorial, define the events and their rankings as shown in Figure 4. Figure 4 Clicking on the Reorder button above the Rank label will reorder the events as shown in Figure 5. Figure 5-7 -

9 Now, input ratios (the ratios are for illustration purposes only) as shown in Figure 6. Figure 6-8 -

10 If you click on the Use button above the Avg. Freq. label the events and the chosen average frequencies will be copied to the main area in range A7:B16 and the bar graph will show the results. See Figure 7. Figure 7-9 -

11 Now input the split fractions shown in Figure 8. Figure 8 If you want to use the average frequencies based on split fractions, click the corresponding Use button (as shown in Figure 8) which will replace the information in range A7:B16 and update the bar graph as shown in Figure 9. Figure

12 NOTE: The remaining step in the DET (elicitation of scaling parameter k) crucially depends on the information in range A7:B16. It is therefore absolutely essential that the information provided reflect the expert s judgments about the events and their average frequencies. Of course, you can always come back to this section and make changes (other sections of the DET will automatically be updated). In some instances it might be helpful for the expert to visualize the ratio of two judgments (e.g., for ratio judgments and split fractions). To facilitate this, the DET contains a standard probability wheel where the user can adjust the two areas by using the slider below the probability wheel (see Figure 10). Figure 10 The user can return to the main menu by clicking on the Return to Main Menu button

13 Defining k Figure

14 This section allows the user to adjust the shape of the individual Beta distributions for each event by adjusting the scaling factor k using the slider beneath the top two graphs. These two graphs show the cumulative distribution function and the density function of the marginal beta of the event chosen from the list box at the top. The other two graphs in this section show the cumulative distribution functions and density functions of ALL events. All graphs automatically update as the user adjusts the slider to provide important visual feedback about the shape of the individual distributions. Note that the range of the x-axis in the top two graphs can be changed by clicking on the Change Scale button. The user can also input comments in the Comments section (one line at a time). For the purpose of this mini-tutorial, choose Ricin as the event for which the scaling parameter k should be fit (the list box is automatically updated depending on the events provided in range A7:A16 in the Define Events section). The DET will show the event name, its average frequency and the current parameters for the beta distribution (a and b). Of course, the latter parameters will change if the user makes adjustments with the slider. Figure 12 NOTE: The sensitivity (range of k s) of the slider can be adjusted by providing a minimum and maximum value for k in the greenly shaded areas beneath the slider. See Figure 13. Figure

15 The DET provides interactive and instructive feedback to facilitate the definition of the scaling factor k. To this end, the user can input various fractiles and their corresponding cumulative probabilities in the greenly shaded area in range A27:B33. Any information provided in this area will show up as points in the plot of the cumulative distribution function of the chosen event. IMPORTANT: Note that the information provided in range A27:B33 will not automatically change if a new event is chosen. For the purpose of this mini-tutorial, input the cumulative probabilities (F(x)) and fractiles (x) as shown in Figure 14 and use the slider to adjust the cumulative beta distribution. Figure

16 The scale of the x-axis in the top two graphs can be changed by clicking on the Change Scale button which opens the dialog box shown in Figure 15 (enter the minimum and maximum values as shown. Figure 15 Click the OK button in the dialog box to close it and the graphs are updated as shown in Figure 16. Figure 16 IMPORTANT: The summary report is based on whatever information (especially the event chosen from the list box and the provided fractiles) is on the screen. For an accurate report of the elicitation it is therefore important to have the event that was chosen for fitting the scaling parameter k on this screen before the report is generated. The user can return to the main menu by clicking on the Return to Main Menu button

17 Summary Report This section provides a summary report of all the user inputs and calculated results. The report can be printed by clicking on the Print Report button. The report will generate three pages as shown (using the information provided in the mini-tutorial) in Figures Figure

18 Figure

19 Figure 19 The user can return to the main menu by clicking on the Return to Main Menu button

20 APPENDIX F Using the Dirichlet Aggregation Tool: A Mini-Tutorial By Thomas Eppel University of California at Irvine Irvine, California Overview The Dirichlet Aggregation Tool (DAT) is a companion to the Dirichlet Elicitation Tool (DET; documented elsewhere) which aggregates the marginal beta distributions of the Dirichlet parameters elicited from a group of experts. For the current version of the DAT to work, the elicitations must have been based on version 2.0 of the DET. The functionality of the DAT is straightforward: the user selects the elicitation files (based on DET Version 2.0) to be aggregated, the DAT will perform the aggregation of the cumulative distribution functions of the beta distributions and generate a report of the aggregation result. Starting the DET It is highly recommended to work with a copy of the DAT. Therefore, either make a copy of the file in the Windows Explorer or choose File Save As in Excel. Make sure that you give the file a meaningful name (e.g., name of the project). Since the DAT contains VBA code, you might be asked whether or not you want to enable Macros when you load the file (this depends on the specific configuration of Excel on your computer). Make sure that you enable the Macros

21 Main Menu Figure 1 The Main Menu provides access to the three main modules of the DET: Add Experts: Click on this button to select the files of the elicitation sessions to be aggregated. Aggregate: Click on this button to have the DAT perform the aggregation. Show Results: Click on this button to generate a report of the aggregation results

22 Adding Experts Figure 2 After clicking on the Add Experts button on the main screen, you will see the window shown in Figure 2. You can use this standard Windows Open File dialog to navigate to the folder that contains the elicitation files to be aggregated. Select the (first) file and click the Open button to load the file into the DAT. You will then be asked whether you want to add more files (see Figure 3). Click Yes if you want to add another expert s file (which will open another Open File dialog). Continue to add files until all the files have been loaded into the DAT. Then click the No button in the window shown in Figure 3 to get back to the main screen of the DAT

23 Figure 3 NOTE: After the DAT is done reading the elicitation files, it needs to close them. You will see repeated dialogs as shown in Figure 4, asking whether you want to save changes. Since no changes were made to these files, you should choose No to close the dialog. Figure

24 Aggregation The main screen of the DAT now shows the compilation of experts, events, shape parameters k, and average frequencies based on the user s selections of files. Figure 5 The example in Figure 5 shows that there may be inconsistent event descriptions over the experts. For example, some experts may not have used the same partitioning of events (e.g., Expert 3 did not use Event 3 ). Or, there may have been simple typos during the elicitation (e.g., using Event1 for Expert 4). In the above example, the user can clean up the inconsistencies as much as possible. For example, the average for Event 1 for Expert 4 was moved from cell F18 to cell F15 ( Event1 in cell B18 was then deleted). See Figure

25 Figure 6 After the inconsistencies are reconciled, the user can then click the Aggregate button for the DAT to perform the aggregation. Depending on the number of events and experts, this may take some time during the screen may switch back and forth between different windows

26 Generate Report After the aggregation is performed, the user can click on the Show Results button. The DAT will then compile a report of the aggregation results, including graphs of the individual and aggregate cumulative distribution functions as well as the individual density functions of the beta marginals. This report can then be printed by clicking on the Print Report button. See Figure 6. Figure

27 Figure