Most models attempting to estimate or predict some elements of the world, will come with their own estimates of uncertainty. It could be the Standard Model of physics predicting the mass of the Z boson as 91.1874 ± 0.0021 GeV, or the rather wider uncertainty ranges of economic predictions.

In many cases, though, the uncertainties in or about the model dwarf the estimated uncertainty in the model itself - especially for low probability events. This is a problem, because people working with models often try to use the in-model uncertainty and adjust it to get an estimate of the true uncertainty. They often realise the model is unreliable, but don't have a better one, and they have a measure of uncertainty already, so surely doubling and tripling this should do the trick? Surely...

The following three cases are going to be my go-to examples for showing what a mistake this can be; they cover three situations: extreme error, being in the domain of a hard science, and extreme negative impact.