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March 7, 2009

McDaniel v. Brown: The Supreme Court, Bayes' Theorem, Five Brothers, and Two Errors in DNA Probabilities

At the end of January, the Supreme Court granted a petition for the writ of certiorari in McDaniel v. Brown.  I noted this case back in May 2008.  In Brown v. Farwell, 525 F.3d 787 (9th Cir. 2008), as the case then was known, the Ninth Circuit discussed Bayes' Theorem and granted habeas corpus relief. The May blog explained how the majority of the panel may have misportrayed the implications of the theorem in this case.

The Supreme Court will consider two procedural issues: (1) What is the standard of review for a federal habeas court analyzing sufficiency-of-evidence claim under Antiterrorism and Effective Death Penalty Act? (2) Does analysis of sufficiency-of-evidence claim pursuant to Jackson v. Virginia under 28 U.S.C. § 2254(d)(1) permit federal habeas court to expand record or consider nonrecord evidence to determine reliability of testimony and evidence given at trial? The "nonrecord evidence" is a report prepared by Dr. Larry Mueller pointing out errors in the trial testimony of the DNA analyst, Renee Romero, about the "prosecutor's fallacy" and the chance of a match to one of the defendant's brothers. Mueller is correct on both counts. First, Romero, at the behest of the prosecutor, transposed the conditional probability of a match to an unrelated individual given that the defendant was the source of the DNA by transforming it into "a 99.99967 percent chance that Troy's DNA was the same as the DNA discovered in Jane's underwear." Because the uncontested random-match probability was 1/3,000,000, however, a correct application of Bayes' Theorem easily could give approximately the same result. (This point is explained in the earlier blog.) Second, Romero miscomputed the chance of a match to one of Troy's untested brothers as 1/6500. As Mueller found, the correct number is closer to 1/66.

If the Court agrees that Mueller's report should have been ignored, then an interesting evidence question arises. Can a court take judicial notice that Romero's testimony about the probabilities was wrong? I think so. The transposition error has been discussed ad nauseum in the scientific-evidence literature. See, e.g., The New Wigmore: A Treatise on Evidence: Expert Evidence (2004). Mueller's figure of 1/66 is trickier, though, because it rests not only on a well-accepted formula in genetics but also on sample data about allele frequencies. Still, the proposition that Romero's figure of 1/6500 is too small is indisputable. As noted in the May blog, the correct number cannot be much smaller than 1/512 for the two brothers considered by Romero (or 1/256 for these two plus another living across the state line). Of course, whether these errors -- errors that were not brought out at trial -- can be shoehorned into a grounds for habeas relief is another question that I shall leave for others to address.

--DHK

Acknowledgements: Thanks to Carissa Hessick for calling the grant of certiorari to my attention and to Larry Mueller for explaining his analysis of the probability for a match to a brother.

March 7, 2009 | Permalink

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