# 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?

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One might temper this sort of reasoning, which is based solely on counts, by considering the differences between (i) a huge database that contains no immediate members of a person's family and (ii) a database that contains only members of a person's family. These extreme examples further suggest that the amount of "evidential value" may depend on whether the result is or is not a hit and on what conclusions are being drawn as a result. These examples also show that the question requires more information about the probability model one has in mind for matching. –  whuber May 14 '12 at 15:48
In your last paragraph are you implicitly comparing two models where you have a sample of 16 million and a population of (how many?): A), where an event occurs one in a million and B) where an event is unique in the population? And you want to decide whether A or B is more plausible, given an observation of one event out of 16 million? –  Peter Ellis May 17 '12 at 1:02
Is there a chance of a spurious match? Can a large enough database give you two matches and what'd you do then? –  curious_cat Mar 11 at 12:26

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.

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