When conclusions based on statistical science are drawn from data, it is crucial that
the data and the reasoning supporting those conclusions are transparent. Under the
term ‘intelligent transparency’ Baroness Onora O’Neill5 has argued that the data
and reasoning must be:
• accessible: ie easily available and not, for example, hidden behind a proprietary algorithm;
• understandable: to everyone involved in the case, including a jury;
• useable: they address current specific concerns; and
• assessable: where the ‘working’ is open to scrutiny by legal and other professionals.
The prosecutor's fallacy occurs when the probability of the evidence (matching DNA
profile, glass fragment of the same refractive index as the fragment recovered from
the target window, etc) given innocence (the random match probability) is incorrectly
interpreted as the probability of innocence given the evidence. This is formally known
as ‘transposing the conditional’, and is a clear breach of logic that becomes obvious
when the correct statement ‘If it’s a dog, the chances are very high that it has four legs’
is transposed to ‘If an animal has four legs, the chances are very high that it’s a dog’.
Some ideas (quotes from the document)