Undergrad Does this defense lawyer's probability argument sound like BS?

[swampwiz]

Either that, or the author is a typical "pop scientist" author that doesn't understand probability too well.

https://nautil.us/issue/4/the-unlikely/the-odds-of-innocence

 

[willem2]

Either that, or the author is a typical "pop scientist" author that doesn't understand probability too well.

https://nautil.us/issue/4/the-unlikely/the-odds-of-innocence

What's wrong with it? This seems like an ok application of Bayes theorem.
The main problems with this kind of calculation are the difficulty of establishing the prior probability that someone is guilty, and the interpretation of the result. (What percentage was reasonable doubt again, your honour?)

 

[mjc123]

The general point seems sound to me, but I'd have a couple of objections;
1. General: most people don't have a good enough understanding of probability to properly evaluate the arguments.
2. Specific: I'm not happy with the initial assumption of guilt of 1/200000. That seems to assume he was randomly selected from the local population to be put on trial, or at least to have his DNA tested, but that isn't the case. He was a known sex offender, and therefore likely to be of interest as a suspect, and his DNA was already on the database and found to be a match. He was not a random choice.

 

[FactChecker]

I would have to think about the defence's likelihood ratio argument. I have never seen a likelihood ratio interpreted as a probability. I think that may be an error. Or it may be using the term "likelihood" in a different context than I am used to.

 

[Dale]

Specific: I'm not happy with the initial assumption of guilt of 1/200000. That seems to assume he was randomly selected from the local population to be put on trial, or at least to have his DNA tested, but that isn't the case. He was a known sex offender, and therefore likely to be of interest as a suspect, and his DNA was already on the database and found to be a match. He was not a random choice.

I think that is a good point. Probably the beat approach would have been to start with the “random male” number but add “convicted sex offender” as an additional explicit piece of evidence.

 

[Dale]

I would have to think about the defence's likelihood ratio argument. I have never seen a likelihood ratio interpreted as a probability. I think that may be an error. Or it may be using the term "likelihood" in a different context than I am used to.

The likelihood ratio isn’t a probability because it can be greater than 1. It is the strength of the evidence. If you multiply the prior odds by the likelihood ratio then you get the posterior odds.