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skepsci comments on Hearsay, Double Hearsay, and Bayesian Updates - Less Wrong
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It proves that mistakes have been made, but in the end, no, I don't think it's terribly useful evidence for evaluating the rate of wrongful convictions. Why not? There have been 289 post-conviction DNA exonerations in US history, mostly in the last 15 years. That gives a rate of under 20 per year. Suppose 10,000 people a year are incarcerated for the types of crime that DNA exoneration is most likely to be possible for, namely murder and rape (I couldn't find exact figures, but I suspect the real number is at least this big). Then considering DNA exonerations gives us a lower bound of something like .2% on the error rate of US courts.
That is only useful evidence about the error rate if your prior estimate of the inaccuracy was less than that, and I mean, come on, really? Only one conviction in 500 is a mistake?
DNA exoneration happens when one is innocent and combination of extremely lucky circumstances make retesting of evidence possible. The latter I would be shocked to find at higher than 1:100 chance.
The appellate system itself - of which cases involving new DNA evidence are a tiny fraction - is a much more useful measure.
There are a whole lot more exonerations via the appeals process than those driven by DNA evidence alone. This aught to be obvious, and the 0.2% provided by DNA is an extreme lower bound, not the actual rate of error correction.
Case in point, I found an article describing a study on overturning death penalty convictions, and they found that 7% of convictions were overturned on re-trial, and 75% of sentences were reduced from the death penalty upon re-trial.
One in fourteen sounds a lot more reasonable to me, and again that's just death penalty cases, for which you'd expect a higher than normal standard for conviction and sentencing.
The standard estimate is about 10% for the system as a whole.