Quantification of Prior Knowledge Through Subjective Probability Assessment

Appendices

Appendix 4.1: Questionnaire for Implementing the Equivalent Lottery Method

This appendix provides a questionnaire for implementing the equivalent lottery method. The questionnaire starts with a question (i.e., Q1), that is used to determine a reference prize for the equivalent lottery method, followed by the second and third questions (i.e., Q2 and Q3) for determining 1 % and 99 % percentiles (i.e., $\theta_{i,0.01}$ and $\theta_{i,0.99}$) of the variable $\theta_{i}$ concerned, respectively. Then, the fourth question (i.e., Q4) can be used to estimate the 50 % percentile (i.e., $\theta_{i,0.5}$) of $\theta_{i}$ if sufficient information on $\theta_{i}$ is available. The questionnaire can be continued to determine percentiles of $\theta_{i}$ progressively until engineers believe that there is no sufficient information on $\theta_{i}$ to balance the two lotteries in the equivalent lottery method for a given range of $\theta_{i}$.

Questionnaire

• Q1: What is the prize that you want recently? Please write it down.

• Answer: $A_{1}$

• Q2: What is the minimum possible value of $\theta_{i}$?

• Answer: $A_{2}$

• Q3: What is the maximum possible value of $\theta_{i}$ ?

• Answer: $A_{3}$

• Q4: There are two lotteries as follows.

• Lottery 1:

  • Win $A_{1}$ if $A_{2} \le \theta_{i} \le a_{s}$ occurs.

  • Win nothing if $a_{s} < \theta_{i} \le A_{3}$ occurs.

• Lottery 2:

  • Win $A_{1}$ or nothing equally likely.

Please adjust the value a _s from $A_{3}$ to $A_{2}$ gradually until you feel indifferent between the two lotteries. Please write down the resulting value of a _s and denote it by $A_{4}$.

Note that the questionnaire shall be continued to determine percentiles of $\theta_{i}$ progressively using different ranges of $\theta_{i}$ in the equivalent lottery method if there is sufficient information on $\theta_{i}$ to balance the two lotteries for a given range of $\theta_{i}$.