# 2.3.2 Empirical probability vectors

Course subject(s) Module 2. Calibration and Information score

Consider the following table where 3 experts have given their 5%, 50% and 95% quantiles for 5 different questions.

A Dutch supermarket is interested in eating habits among Dutch adults.
For this purpose, three experts have been consulted. First, these experts need to be evaluated based on five calibration questions.

1) What percentage of Dutch adults eats fruit on a daily basis?
2) What percentage of Dutch adults eats fast food less than once a month?
3) Consider the caloric consumption of Dutch adults ten years ago. What is the caloric consumption today, compared to ten years ago? (here, 100% means there was no change)
4) How many liters of milk are consumed on a yearly basis by the average Dutch adult?
5) How many kilos of meat does the average adult consume in six months time?

The answers of the experts are summarized in the table below. For example, for Question 1, Expert 1 estimates this percentage to be 46. Also, (s)he believes that there is 90% chance that the percentage is between  44 and 49. The realization, based on actual research, turned out to be 50 (Note that the data are purely fictional).

Question Realization Expert 1

5%   50%  95%

Expert 2

5%   50%  95%

Expert 3

5%   50%  95%

1 50 44    46    49 30    40    55 38    47    55
2 7 9    12    15 1    15    20 2     8     17
3 108 102    106    110 60    80    95 91    99    106
4 66 55    59    64 53    70    80 58   68    75
5 24 28    31    35 10    19    30 26    35    43

Interquantile ranges

Recall from the previous video that the three quantiles provided by experts define 4 interquantile ranges.

IQ1 – smaller than 5% quantile
IQ2 – between the 5% and the 50% quantile
IQ3 – between the 50% and 95% quantile
IQ4 – larger than 95% quantile.

So the realization can fall only in one of the 4 intervals.

Expert empirical probability vector

An empirical probability vector for an expert can be now obtained from the proportion of questions in which the realization falls into one of the 4 interquantile ranges. This is, s=(s_1,s_2,s_3,s_4), where

s_1 = the proportion of questions in which the realization falls in IQ1
s_2 = the proportion of questions in which the realization falls in IQ2
s_3 = the proportion of questions in which the realization falls in IQ3
s_4 = the proportion of questions in which the realization falls in IQ4

Decision Making Under Uncertainty: Introduction to Structured Expert Judgment by TU Delft OpenCourseWare is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License.
Based on a work at https://online-learning.tudelft.nl/courses/decision-making-under-uncertainty-introduction-to-structured-expert-judgment//.