False positives

False positives

Last time we derived one formula for the impact of false positive probability on the value of DNA evidence. Today, we’ll look at seemingly different formula to get a better perspective. Buckleton, Bright, & Taylor (2018) give a formula for the impact of errors on likelihood ratio different from the one we discussed before. Since the derivation is simpler and it turns out that in fact this is simply a more general formula, of which the one we already discussed is just a particular instance, it worth taking a look.

First, Buckleton et al. (2018) make the conceptual distinction between the probability that an error occurs () and the probability that a match is reported if it does. In terms of our notation, we have:

which is the same as the formula obtained by Aitken, Taroni, & Thompson (2003) if we take to be FPP, as we should on the assumption that .

Aitken, C., Taroni, F., & Thompson, W. (2003). How the probability of a false positive affects the value of dna evidence. Journal of Forensic Science, 48(1), 1–8. https://doi.org/10.1520/jfs2001171

Buckleton, J. S., Bright, J.-A., & Taylor, D. (2018). Forensic dna evidence interpretation. CRC press.