Tuesday, March 6, 2018

Transposing Likelihoods (Again)

In the panels below are descriptions from appellate court opinions of testimony about likelihood ratios. Can you spot the one in which the explanation of the numerical value of the ratio or its components is different from the others? Which version is correct? The answers are posted separately.
[T]he DNA sample taken from the gun's grip was at least 384 times more probable if the sample originated from Appellant and two unknown, unrelated individuals than if it originated from a relative to Appellant and two unknown, unrelated individuals. Therefore, the laboratory concluded there was “strong support” that Appellant contributed to this mixture. Testing of the DNA sample retrieved from the gun's magazine also yielded the conclusion that the DNA sample was at least 29 times more probable if the sample originated from Appellant and two unknown, unrelated individuals than if it originated from a relative to Appellant and two unknown, unrelated individuals.

Commonwealth v. McClellan, No. 2014 EDA 2016, 2018 WL 560762 (Pa. Super. Jan. 26, 2018)
DNA from sperm cells found on the vaginal swabs was compared to defendant's and Barbara's DNA. A forensic scientist testified that Barbara and defendant could not be excluded as contributors to the DNA found. The expert also explained it was 18.3 million more times likely the DNA found was defendant's as compared to the African–American population, 208 million times more likely as compared to the Caucasian population, and 26.2 million times more likely as compared to the Hispanic population. The analyst explained that “when you have a likelihood ratio greater than 1,000, that lends very strong support” that it is the person's DNA


State v. R.B., NO. A–0736–15T1, 2018 WL 345844 (N.J. Super. App. Div. Jan. 10, 2018)
During trial, multiple witnesses testified that Washington could not be excluded as a contributor to DNA that was recovered from the fingernail piece and other evidence. Dr. [Ranajit] Chakraborty testified as an expert in “likelihood ratio computation,” which he explained was a “technical concept” that examines “multiple scenarios” that could explain a given DNA test result and then determines, based on statistical analysis, “which scenario explains the observation best.” According to Chakraborty, this analysis results in a more accurate determination of how likely a certain individual could be excluded as a contributor of a particular DNA sample. Over Washington's objection that this analysis had not been sufficiently peer-reviewed and was thus unreliable, Chakraborty testified that there was a 1 in “at least” 1,000,000,000,000,000 chance that the DNA profile of the major contributor found in the DNA mixture obtained from the fingernail piece would be someone other than Washington.

Washington v. State, No. 03–15–00531–CR, 2017 WL 3903019 (Tex. App. Aug. 31, 2017) (unpublished)
Lee, trained to calculate the likelihood ratio statistic, used data provided by the Identifiler Plus kit manufacturer reporting the frequency of alleles for three racial groups in the United States to determine: (1) it was 140 million times more likely that the DNA sample originated from Casey, defendant, and one unknown individual, rather than from Casey and two unknown individuals in the African American population; (2) it was 6 billion times more likely that the DNA sample originated from Casey, defendant, and one unknown individual, rather than from Casey and two other individuals in the Hispanic population; and (3) it was 1.2 trillion times more likely that the DNA sample originated from Casey, defendant, and one unknown individual, rather than from Casey and two unknown individuals in the Caucasian population.




People v. Easton, No. H041704, 2017 WL 393263 (Cal. App. Jan. 30, 2017) (unpublished)

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