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In this article, we analyze a problem related to DNA evidence that is likely to be of great and increasing significance in the near future. This is the problem of whether, and how, to present evidence that the suspect has been identified through a DNA database search. In our view, the two well-known reports on DNA evidence issued by the National Research Council (NRC) have been badly mistaken in their analysis of this problem. The mistakes are significant because the reports have carried great authority with American courts; moreover, the DNA Advisory Board of the FBI has endorsed the second report on this issue. We will also offer some reflections on the habits of mind, of both lawyers and statisticians, that may have led to this result.