Compare this statement of the likelihood ratio to the misstated version from a “senior science writer” for Forensic Magazine:[I]nvestigators didn't have a sample of DeAngelo's DNA, so Sacramento sheriff's detectives began following him as he moved about town, finally watching April 18 as DeAngelo parked his car in a public parking lot at a Hobby Lobby store in Roseville, according to an arrest warrant affidavit unsealed Friday.
"A swab was collected from the door handle while DeAngelo was inside the store," according to the affidavit from sheriff's Detective Sgt. Ken Clark. "This car door swab was submitted to the Sacramento DA crime lab for DNA testing." ... The swab contained DNA from three different people, and 47 percent of the DNA came from one person, the affidavit said.
That DNA was compared to murders in Orange and Ventura counties where DNA had been collected and saved from decades before, and it came back with results that elated investigators. "The likelihood ratio for the three-person mixture can be expressed as at least 10 billion times more likely to obtain the DNA results if the contributor was the same as the Orange County/Ventura County (redacted) profile and two unknown and unrelated individuals than if three unknown and unrelated individuals were the contributors," Clark wrote in his affidavit seeking an arrest warrant for DeAngelo. ...
Sacramento County District Attorney Anne Marie Schubert has said previously that even with the possible match she asked for a better sample, so investigators went hunting again, this time focusing on DeAngelo's trash on April 23.
"The trash can was put out on the street in front of his house the night before," Clark wrote. "DeAngelo is the only male ever seen at the residence during the surveillance of his home which has occurred over the last three days."
Detectives gathered "multiple samples" from the trash can and sent them to the crime lab on Broadway for analysis. "Only one item, a piece of tissue (item #234-#8), provided interpretable DNA results," Clark wrote."The likelihood ratio for this sample can be expressed as at least 47.5 Septillion times more likely to obtain the DNA results if the contributor was the same as the Orange County/Ventura County (redacted) profile than if an unknown and unrelated individual is the contributor." 2/
To see the error, click on the label “transposition” in this blog. Of course, one can ask what’s the big deal when the likelihood ratio is in the septillions. But that question translates into an argument about harmless error. Sometimes the errors associated with sloppy phrasing won’t have immediate repercussions, but a magazine written for forensic practitioners ought not propagate sloppy thinking. In any case, things are looking up when detectives take the care to avoid transposing their conditional probabilities.The warrants now show that: ... [t]he additional surreptitious sample was from DeAngelo’s trash can set out at the curb. Only one piece of tissue provided interpretable DNA results, but those translated to a likelihood that DeAngelo was 47.5 septillion times more likely to be the Golden State Killer than an unknown and unrelated individual. 3/
NOTES
- Sam Stanton & Darrell Smith, Read the Warrant Documents in the East Area Rapist Case, Sacramento Bee, June 1, 2018, http://www.sacbee.com/news/local/article212377094.html
- Sam Stanton & Darrell Smith, How Detectives Collected DNA Samples from the East Area Rapist Suspect, Sacramento Bee, June 1, 2018, http://www.sacbee.com/latest-news/article212334279.html
- Seth Augenstein, Golden State Killer Warrants Show Evolution of Killer — But Not Genealogy, Forensic Mag., June 4, 2018, https://www.forensicmag.com/news/2018/06/golden-state-killer-warrants-show-evolution-killer-not-genealogy
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