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Poor probabilistic reasoning can ruin lives

February 24, 2010

Via Ta-Nehisi Coates comes Michael Bobelian’s DNA’s Dirty Little Secret:

Typically, law enforcement and prosecutors rely on FBI estimates for the rarity of a given DNA profile–a figure can be as remote as one in many trillions when investigators have all thirteen markers to work with. In Puckett’s case, where there were only five and a half markers available, the San Francisco crime lab put the figure at one in 1.1 million–still remote enough to erase any reasonable doubt of his guilt. The problem is that, according to most scientists, this statistic is only relevant when DNA material is used to link a crime directly to a suspect identified through eyewitness testimony or other evidence. In cases where a suspect is found by searching through large databases, the chances of accidentally hitting on the wrong person are orders of magnitude higher.
The reasons for this aren’t difficult to grasp: consider what happens when you take a DNA profile that has a rarity of one in a million and run it through a database that contains a million people; chances are you’ll get a coincidental match. Given this fact, the two leading scientific bodies that have studied the issue–the National Research Council and the FBI’s DNA advisory board–have recommended that law enforcement and prosecutors calculate the probability of a coincidental match differently in cold-hit cases. In particular, they recommend multiplying the FBI’s rarity statistic by the number of profiles in the database, to arrive at a figure known as the Database Match Probability. When this formula is applied to Puckett’s case (where a profile with a rarity of one in 1.1 million was run through a database of 338,000 offenders) the chances of a coincidental match climb to one in three.

Also see the tragic case of Sally Clark, who was convicted of murdering her infant children because the expert witness (a pediatrician) didn’t understand the importance of the independence assumption nor conditioning on all covariates when calculating probabilities. Clark was sent to prison, where her status as a child-killer made her a target for other prisoners. A few years after her release (the prosecutor had suppressed exonerating evidence), she died of acute alcohol poisoning.

So, my recent obsession with most people’s inability to think probabilistically is not so esoteric after all.

First thought: A degree in Statistics grants you a certain degree of immunity to incompetent/deceptive prosectors.

Second thought: I have jury duty coming up. I wonder if “I am pursuing a Master’s degree in Statistics” will make me more or less likely to be selected to a jury?


From → Probability

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