“Watermelons” by Ahmad is licensed under CC BY-NC 2.0

What is the percentage of water in watermelon?

To answer this question, we consult two experts (expert A & expert B).  Each expert gives their 5%, 50% and 95% quantiles which can be seen in the table below.

Expert	5%	50%	95%
Expert A	80	90	94
Expert B	93	95	97

Recall that, with their assessments, the experts are sending the following message:

Expert A:
– the median (50% quantile) estimate is 90, so (s)he believes that 90% is the best estimate for the percent of water in the watermelon. (S)he believes there is a 50% chance that the true water percentage  is below or above 90.
– the lower bound (5% quantile) is 80, the is, (s)he believes there is a 5% chance that the true water percentage is below 80%.
– the upper bound (95%) is 94 the is, (s)he believes there is a 5% chance that the true water percentage is above 94%.

Concluding, according to expert A assessments, her/his best estimate is 90% and her/his uncertainty is given by the credible interval (80%,94%), that is, (s)he believes there is 90% chance that the true water percentage is between 80% and 94%.

Expert B:
– the median (50% quantile) estimate is 95, so (s)he believes that 95% is the best estimate for the percent of water in the watermelon. (S)he believes there is a 50% chance that the true water percentage  is below or above 95.
– the lower bound (5% quantile) is 93, the is, (s)he believes there is a 5% chance that the true water percentage is below 93%.
– the upper bound (95%) is 97 the is, (s)he believes there is a 5% chance that the true water percentage is above 97%.

Concluding, according to expert B assessments, her/his best estimate is 95% and her/his uncertainty is given by the credible interval (93%,97%), that is, (s)he believes there is 90% chance that the true water percentage is between 93% and 97%.

What is the percentage of water in watermelon? We now know that the true value is 92%!