'The procecutor's falicy': abduction and probability

[matt grime]

I think you have that wrong. The probability that you left that DNA evidence based on the DNA alone is 1 in 65. If you want to factor in other evidence then by all means do, however it is the correct probabilistic interpretation of the DNA evidence and is not a fallacy. It does not assume that each person with that matching sample was in the area, it assumes that they are equally likely to have been in the area, which is reasonable unless you can show otherwise.

[Heretic]

I hope something is wrong with those numbers. If 1/100 people can be linked to DNA some a random source, we need a FAR better system. If that's true DNA evidence isn't showing you who the suspect is, it's merely eliminating 99% of the possibilities. That's really not enough to base an entire case after, like so many prosecutors have.

 

EDIT: Missed Page 2 for some reason...

 

I have to agree with Matt it's more a 1/65. The odds that more people with the same DNA live in the same area is VERY HIGH. For example, when I grew up with my 2 brothers, my mother and father there is at least 2 people (my brothers) with very similar DNA.

 

My mother grew up in a small town (3000) with 7 siblings and almost 20 cousins. Her odds of having DNA mixed up would be a lot higher I would assume.

 

So basically unless it's an alien with no relatives in the country, you can't be sure you have the right guy based on DNA or proximity.

[Dak]

I'd have thought that, given the population distribution, the probability of the other's being in the area would be so low as to make the assumption that they were unjustified.

 

No wait, i see your point. the knowledge that the guy was in the area is based on other evidence, outside of the DNA profile, to prove that he was in the area, whereupon we become justified in assuming that the others probably weren't (without the other evidence, we must also assume that he probably wasn't).

 

hmm... how about this:

 

the chances of a coincidental match are 1/100.

 

there are 1000 people in the UK (just to make it easyer).

 

therefore, without concidering any other evidence and based only on the DNA profile, there is a 1/10 chance that the suspect is guilty.

 

then could we stack other evidence on top of it, and use the 1/10 figure as an a prior assumption of guilt to use bayes theorum to factor in the other evidence (if it renders nicely to stats)? and keep altering the presumption by running it through bayes theorum untill all the evedence had modified the presumption to give a final posteria probibility?

 

Oh, and in case anyone is now in fear of our legal system, dont worry: most forensic scientists are taught to steer clear of all but the simplest of statistical analysis, unless they are specifically trained. We hire statistitions to do this for us when neccesary.

[Dak]

I hope something is wrong with those numbers. If 1/100 people can be linked to DNA some a random source, we need a FAR better system. If that's true DNA evidence isn't showing you who the suspect is, it's merely eliminating 99% of the possibilities. That's really not enough to base an entire case after, like so many prosecutors have.

 

The number is artificially low, to make the example easyer.

 

Usually, the number is one in at least a couple-hundered million. it usually goes up to 1 in several billion, and even hits the trilllions quite often.

 

I have to agree with Matt it's more a 1/65. The odds that more people with the same DNA live in the same area is VERY HIGH. For example, when I grew up with my 2 brothers, my mother and father there is at least 2 people (my brothers) with very similar DNA.

 

My mother grew up in a small town (3000) with 7 siblings and almost 20 cousins. Her odds of having DNA mixed up would be a lot higher I would assume.

 

So basically unless it's an alien with no relatives in the country, you can't be sure you have the right guy based on DNA or proximity.

 

your only 50% similar to either parent, and to your siblings. it's only a problem in the case of identical twins.

 

extremely infrequent alleles are given an artificially high prevalence (e.g. if it's frequency is <0.001%, i believe it is taken to have a(n artificially raised) frequency of 0.001), specifically to prevent people from families/locations where the allele is present from having unrepresentatively 'inprobable' profiles.

 

I kinda agree with your concern for the potential for error tho. tbh, i dont see why a bio-statistition doesn't just forumulate a calculation that takes all of this into account, and have someone whack a program together that gives a nice probabalistic weghting of the significance of the profile (afaik this is not the case). It seems a lot easyer and less prone to error than leaving the stats up to biologists and lawyers, neither of whom are guaranteed to be any good at stats.

[matt grime]

Don't confuse the DNA tests were talking about here with a complete DNA analysis. Matching DNA tests do not mean matching DNA. The former just splits the DNA up into chunks and measures the lengths of the chunks. It produces approximately a 1/1,000,000 (or at least when I did probability 10 years ago that is the number bandied around; they may have a better test now) chance of matching you to someone else. A complete DNA analysis, a full sequencing would be essentially unique, but impractical to do (for time and expense reasons; one of these basic DNA tests takes a week to do, not 10 minutes a la CSI).

[Dak]

the art has progressed a bit in the last ten years

 

It sounds like your describing restriction fragment length polymorphism profiling. Short tandem repeat profiling is used now: it takes about 3 hours, i believe (never actually stood by the machine as it was doing its stuff), and is much more specific to an individual (the FBI use 1 in 260 billion as a cut off point -- if it's less likely than that, they concider the DNA to be a match).

 

Not sure about a fingerprint ever taking a week to make?