Dawid & Mortera's paper "Coherent Analysis"

Extract from the paper

The part of this paper that is really interesting to me is § 8.3 Use of Databases in which they outline how to treat the database itself — the allele reference sample from the population — as part of the evidence.

Consider, for example, a simple model for a homogeneous population, with the (χi) initially exchangable, having de Finetti representation ... with β(a, b) prior:

The symbol ∝ means proportional to.
dF(p) ∝ pa-1 (1-p)b-1dp.

Suppose that the database δ is of size n, containing r instances of [the crime scene type]. There is also the finding on the suspect [having the crime scene type] so ...

[matching probability]=(r+1+a)/(n+1+a+b) .

For small a and b, this is approximately equivalent to adding the suspect to the database and using (approximately) relative frequency estimates. For large r and n, the effect of conditioning on the suspect becomes unimportant.

Applications and comments on the β distribution

Given that

β(p;a,b) ∝ pa−1(1−p)b−1

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