Talking probabilities: communicating probabilistic information with words and numbers

1. Talking probabilities: communicating probabilistic information with words and numbers Silja Renooij, Cilia Witteman Presented by: Jiangbo Dang

2. Outline • Motivation • Related works • Four experiments • Results and discussions • Conclusion • Additional references

3. Motivation • Numerical probabilities is often considered a major obstacle in the construction of a Bayesian Network • Verbal probabilities are perceived as more natural than numerical probabilities, easier to understand and communicate and better suited to convey the vagueness of opinions • A combination of a numerical probability scale with a verbal probability scale may help to remove the mentioned obstacle

4. Why obstacle • On the input side, it may be a prohibitive quantity of probabilities for all variables in Bayesian network. Experts are reluctant to express them in numerical form, they find it difficult to attach a number to their beliefs. • On the output side, explanation of the results in term of variables with numerical probabilities may be un- comfortable.

5. Related work • Translate numerical probabilities into words and vice versa • Compare Verbal probability expressions with numerical probability expressions under certain situations (Physician prefer verbal to number) • Limit the number of verbal expression in a scale

6. Four experiments • Collect a list of commonly used verbal probability expressions • Determine a rank order for probability expressions from previous experiment • Rate difference between those expressions and develop a scale • Test the translations of the verbal probability expressions into the calculated numerical probabilities.

7. 1. Collect verbal probability expressions

8. 2. Rank probability expressions

9. 3. Rate distances between those expressions • Pairwise comparison (28 pairs for 8 expressions) • Produce co-ordinates for expressions, those co-ordinates best fit the distances given by different subjects • Map co-ordinates onto a probability scale by setting certain and impossible representing 100% and 0%

10. 3. Rate distances between those expressions

11. 3. Rate distances between those expressions

12. 4. Test probability scale

13. 4. Test probability scale • Compare the decisions subjects made when they are using probability in verbal form to their decisions when they are using numerical probability.

14. Conclusion • A probability scale with mutually exchangeable verbal and numerical probability expressions is helpful in BN constructions • Numbers may be just as vague as words for expressing uncertainty • Shortcoming: Dutch subjects and Dutch words

15. References • Cilia Witteman, Silja Renooij. “Evaluation of a verbal-numerical probability scale” • L. C. van at el. “Probabilities for a probabilistic network: a case study in oesophageal cancer”