Is the probability of a unique DNA match the same, irrespective of the size of the dataset? One can argue that the evidential value of a database hit increases when the database gets larger. Indeed, having a unique hit in a database simply means that all the other persons in the database are innocent. Therefore, if the database is larger we have the extra information that many more people are innocent. Clearly, this increases the weight of the evidence against
the suspect.


*

*Is this reasoning correct? 

*Is the probability of a unique match the same, irrespective of the size of the dataset?
This is how I see it: if the database contains everybody, then a unique hits tells us
with certainty who the donor of the DNA prole is. So it really is true that a larger database is stronger evidence. But then I started thinking: suppose the database consists of 16,000,000 proles, and suppose that the DNA prole we are looking for has frequency 1/1,000,000 (one in a million). Is it still reasonable to believe that the underlying model is correct?
 A: Not sure what do you mean with DNA prole.
But a DNA profile with a frequency of 1/1,000,000 is a very bad profile.
Forensic DNA profiles are based in highly polymorphic regions of the DNA.
Not one region: at least 13 different regions.
Therefore, if you find a match in your database you can assume at least that the suspect or a close relative (including monocygotic twins) was the perpetrator, and that's independent of the size of your database.
Of course, the bigger the database the higher the chances of finding a match.
A: Keep in mind that the case against a suspect is stronger in a database match than in a so called cold" case, but contrary to a popular idea, this is not because likelihood ratio increases when compared to a cold case, but because posterior odds are higher in the database case.
A: I am no expert on how these profiles actually work, so I can't comment on that. However, I can comment on this:

This is how I see it: if the database contains everybody, then a unique hits tells us with certainty who the donor of the DNA prole is. So it really is true that a larger database is stronger evidence.

Here you assume that when you have a larger database, you will not obtain more hits (e.g. the number of hits is at most 1). If this is the case (and I certainly hope it is), having a small database yields just as much evidence as a large one when a hit occurs.
