# AMBIGUITY

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## AMBIGUITY

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1. UNCERTAINTY 4: How to do an Expert Judgment Study AMBIGUITY Roger Cooke Resources for the Future Dept. Math, Delft Univ. of Technology April 15,16 2008 INDECISION

2. Uncertainty Ambiguity Indecision 4 Procedures Guide:EUR_18820_ProcGuide.pdf, TABLE OF CONTENTS PART I Generic Issues 1. What is Uncertainty 2. When and how Should Uncertainty Analysis be Performed? 3. Structured Expert Judgment 4. Performance Measures 5. Combinations of Expert Judgments 6. Dependence PART II Procedures 1. Introduction 2. Preparation for Elicitation 3. Elicitation 4. Post-Elicitation APPENDIX I Summary Results of the EC-USNRC Uncertainty Study APPENDIX II ec/usnrc project reports APPENDIX III Glossary of terms for Uncertainty Analysis APPENDIX V Training material REFERENCES

3. Uncertainty Ambiguity Indecision 4 Calibration For each variable Xi, i = 1..n Assess: __ai___ __bi___ __ci___ 5% 50% 95% Expert believes p1 =Prob(Xi ai) = 0.05, p2 = Prob(ai<Xi bi = 0.45), etc Let x1…xn be realizations of X1…Xn s1 = #{i | xi ai} / n, s2 = #{i | ai<Xi bi} / n, etc Then 2n i=1..4 siln (si / pi) ~ Chi square, 3df.

4. Uncertainty Ambiguity Indecision An observation outside is infinitely surprising: disables statistical treatment 4 Why not Triangular?

5. Calibration Score Uncertainty Calibration score Cal(e) = Upper tail probability Ambiguity Indecision 4

6. Uncertainty Ambiguity Indecision Endpoints determined by k% overshoot rule 4 Information score: • For item i, expert e, fit density fe,i(x) to background measure, (x), complying with expert’s quantiles, minimizing information wrt background:

7. Compute relative information wrt background: I(e,i) = I(fe,i(x)| (x) ) =…j=1..4 pjln(pj / mj): mj is background measure of interquantile interval j, for item i. Inf score(e) = average information: (1/#items) i I(e,i)

8. Uncertainty Ambiguity Indecision 4 Combined score Significance Level Cal(e)  Inf(e)  1{Cal(e)  } This score is an asymptotically strictly proper scoring rule, ie: Expert maximizes long run expected score by, and only by, stating percentiles which (s)he believes EJshortcourse\sheets\EJCoursenotes-ScoringRules.doc = 1 if calibration  , else = 0

9. Uncertainty Ambiguity Indecision 4 Combining Experts fe,i = expert e's density for variable i. Equal weight decision maker feq(i) = (1/E) e=1..E fe,i Performance Based Combinations Global weight decision maker • proportional to expert’s combined score, (with optimization). fgw(i) = e=1..Ewe fe,i ; e=1..E we = 1. Item weight decision maker • product of calibration and information for each item (with optimization). fiw(i) = e=1..Ewe,i fe,i ; e=1..E we,i = 1. Weight depends on expert, not item Weight depends on Expert and item

10. Uncertainty Ambiguity Indecision 4 Optimization • significance level  is chosen to optimize combined score of DM: f(i) = e=1…E fe,i  Cal(e)  Inf(e)  1{Cal(e)} For each , compute calibration  information; choose  for which this is maximum.

11. Uncertainty Ambiguity Indecision 4 Dependence

12. Uncertainty Ambiguity Indecision 4 Procedures: Pre-Elicitation (1) Definition of case structure (2) Identification of target variables (3) Identification of query variables (4) Identification of performance/seed/calibration variables (5) Identification of experts (6) Selection of experts (7) Definition of elicitation format document (8) Dry run exercise (9) Expert training session Elicitation (10) Expert elicitation session Post-Elicitation (11) Combination of expert assessments (12) Discrepancy and robustness analysis (13) Feed back (14) Post-processing analyses (15) Documentation

13. Uncertainty Ambiguity Indecision 4 Definition of case structure • Which variables are uncertain • Can the uncertainty be quantified by historical and/or measurement data? • Which (hypothetical) measurements would be used to quantify the parameters?

14. Uncertainty Ambiguity Indecision 4 Identification of target variables • The values of the parameters are uncertain. • The uncertainty cannot be quantified with historical and/or measurement data. • The uncertainty is expected to have a significant impact on the uncertainty of one or more endpoints of the model.

15. Uncertainty Ambiguity Indecision 4 Identify query variables • Ask for values of observable or potentially observable quantities. • Formulate questions in a manner consistent with the way in which an expert represents the relevant information in his knowledge base.

16. Uncertainty Ambiguity Indecision 4 Query vbls  Target vbls?

17. Uncertainty Ambiguity Indecision 4 Elicitation format Conditional on < values of factors in the case structure assumptions > Please give the 5%, 50% and 95% quantiles of your uncertainty in < Hypothetical experiment > taking into account that values of < uncertainty set > are unknown.

18. Uncertainty Ambiguity Indecision 4 Choosing Seed Variables Do NOT use almanac questions!

19. UNCERTAINTY AMBIGUITY INDECISION 3 Practical issues • The seed variables should sufficiently cover the case structures for elicitation. Particularly, when one expert panel should tackle different sub fields, seed variables must be provided for all sub fields. • For each panel at least 10 seed variables are needed, preferably more. • Seed variables may be, but need not be identified as such in the elicitation. • If possible, the analyst should be unaware of the values of the seed variables during the elicitation.

20. Uncertainty Ambiguity Indecision 4 Identify expert pool ROUND ROBIN METHOD • names of potential experts are generated within the organization These persons are approached and asked: • what is your background and knowledge base with regard to the subject? • which other persons are knowledgeable with regard to the subject? • The persons named in the first round are approached with the same two questions. • Step 2 is iterated until (a) no new names appear, of (b) it is judged that a sufficiently diverse set of experts is obtained.

21. Uncertainty Ambiguity Indecision 4 Select ExpertsAt LEAST 4, preferably 6-10 Decide and tell them: • Type of assessment task • Remuneration • Distribution of study results • Use of the expert’s name • Feedback of expert judgment data

22. Uncertainty Ambiguity Indecision 4 Regarding names • Expert names and affiliations: published in the study. • All information, including expert names and assessments, is available for competent peer review, but is NOT for unrestricted distribution. • Individual assessments and scoring: available for unrestricted distribution, identified as “expert 1, 2,3,…” etc. • Expert rationales, by expert #: available for unrestricted distribution. • Expert receives feedback on his/her own performance • Further published use of the expert’s name requires the expert’s approval.

23. Uncertainty Ambiguity Indecision 4 Preparation of Elicitation Protocol • ElicitationProtocol_PM2.5.doc • ElicitationProtocol_INVASIVE_SPECIES.doc • NUREGCR-6545-Earlyhealth-VOL2.pdf • Aspinall Briefing Notes.pdf

24. Uncertainty Ambiguity Indecision 4 Dry Run ALWAYS do a dry run: • is the case structure document clear • are the questions clearly formulated • is the additional information provided with each question appreciated • is the time required to complete the elicitation too long or too short.

25. Uncertainty Ambiguity Indecision 4 Expert training Varies according to need and budget: • 30 min intro for each expert • Half day group meeting to discuss case structure and method • Two day meeting • Case structure • Assessment training • Format for experts’ written rationales EUR_18820_ProcGuide.pdf appendix V

26. Uncertainty Ambiguity Indecision 4 Elicitation • Best to have substantive and normative elicitators • Normative: asks questions, probes for reasons • Substantive: captures reasoning, answers substantive questions • Do NOT use remote or electronic elicitation • Do NOT exceed 4 hrs.

27. Uncertainty Ambiguity Indecision 4 Combining experts’ judgments ..\EJ-Programs\Excalibur.exe

28. Uncertainty Ambiguity Indecision 4 Discrepancy Run EXCALIBUR with eq. weights and Discrepancy: Shows how much the experts differ from the “average expert”

29. Uncertainty Ambiguity Indecision 4 Robustness Run Robustness (items) and (experts) to see how loss of item or expert would affect results: is the mean difference wrt original DM smaller than the differences between experts themselves?

30. Uncertainty Ambiguity Indecision 4 Feedback The experts must have access to • their assessments • calibration and information scores • weighing factors • passages in which their name is used. • Conclusions wrt over- or underconfidence • Conclusions wrt tendency to over- or underestimate.

31. Uncertainty Ambiguity Indecision 4 Post-processingprobabilistic inversionGeneric_Prob_Inversion.pdf

32. Uncertainty Ambiguity Indecision 4 Write upEJCoursenotes-ClassicalModel-Boilerplate.doc Introduction what is purpose why EJ, content of this report Background and Methods Experts Variables of interest Seed variables Performance measures and combination Calibration Information Combination Results Tables and graphs Discussion Conclusions / Recommendations

33. Uncertainty Ambiguity Indecision 4 FAQ’s(1) • From an expert: I don't know that • Response: No one knows, if someone knew we would not need to do an expert judgment exercise. We are tying to capture your uncertainty about this variable. If you are very uncertain then you should choose very wide confidence bounds. • From an expert: I can't assess that unless you give me more information. • Response: The information given corresponds with the assumptions of the study. We are trying to get your uncertainty conditional on the assumptions of the study. If you prefer to think of uncertainty conditional on other factors, then you must try to unconditionalize and fold the uncertainty over these other factors into your assessment. • From an expert: I am not the best expert for that. • Response: We don't know who are the best experts. Sometimes the people with the most detailed knowledge are not the best at quantifying their uncertainty. • From an expert:Does that answer look OK? • Response: You are the expert, not me. • From the problem owner:So you are going to score these experts like school children? • Response: If this is not a serious matter for you, then forget it. If it is serious, then we must take the quantification of uncertainty seriously. Without scoring we can never validate our experts or the combination of their assessments.

34. Uncertainty Ambiguity Indecision 4 FAQ’s(2) • From the problem owner:The experts will never stand for it. • Response We've done it many times, the experts actually like it. • From the problem owner:Expert number 4 gave crazy assessments, who was that guy? • Response: You are paying for the study, you own the data, and if you really want to know I will tell you. But you don't need to know, and knowing will not make things easier for you. Reflect first whether you really want to know this. • From the problem owner: How can I give an expert weight zero? • Response:Zero weight does not mean zero value. It simply means that this expert's knowledge was already contributed by other experts and adding this expert would only add a bit of noise. The value of unweighted experts is seen in the robustness of our answers against loss of experts. Everyone understands this when it is properly explained. • From the problem owner:How can I give weight one to a single expert? • Response: By giving all the others weight zero, see previous response. • From the problem owner: I prefer to use the equal weight combination. • Response: So long as the calibration of the equal weight combination is acceptable, there is no scientific objection to doing this. Our job as analyst is to indicate the best combination, according to the performance criteria, and to say what other combinations are scientifically acceptable.

35. Uncertainty Ambiguity Indecision 4 Lets have another break