Using Bayes Theorem in a Court Case - dementia and testamentary capacity

Question

I'm trying to learn how to use Bayes theorem to explain probabilities in court cases related to dementia and testamentary capacity.

Let's say that we are trying to explain the probability for a person who has dementia to have testamentary capacity, how would one build a Bayes model for this purpose?

I'm thinking something like this:

H = Person does not have testamentary capacity? //Question: Should this be a random healthy person or a person with Dementia?

J = Persons with Dementia?

A = Person does have testamentary capacity?

P(H|J) = P(J|H) P(H) / ( P(J|H)P(H) + P(J|A)P(A) )

P(Person does not have testamentary capacity|Dementia) =

P(Dementia|Person does not have testamentary capacity) * P(Random Person does not have testamentary capacity) /

( P(Dementia|Person does not have testamentary capacity) * P(Random Person does not have testamentary capacity) + P(Dementia|Person does have testamentary capacity)*P(Random Person does have testamentary capacity)

Am I doing it right or wrong?

Thanks for helping out!

Answer 1

I presume you are concerned with cases where a witness is called to give testimony but there is doubt about whether their testimony is acceptable, because they suffer from dementia and this affects their memory of events.

I'm not sure how using Bayes is going to help here. I understand that you are interested in the quantity P(H|J) but I don't see why you would want to try to calculate this from P(J|H). Indeed, P(J|H) is quite a strange quantity. If you know its value, it suggests a study has been done in which a representative sample of people who lack testamentary capacity has been assembled and then the sample has been assessed as to what proportion of them has dementia. Is it really likely that you have such data? It seems more likely that you have direct access to P(H|J) via data about how reliable the memories of people with dementia are.

One might also ask whether appeal to the general frequency represented by P(H|J) is really relevant. If we are talking of a specific person with dementia who has been called as a witness in a case, would it not be better to establish of this particular witness just how reliable their memories are, rather than talking in generalities?

Answer 2

So, Philosophy101, now that you had you fun, I have a question for you: What are we supposed to do now?..

I've been trying to explain insanity to the insane for some time now... just like Socrates tried, or Buddha... And I can't say that I'm doing much worse, because their success rate were almost(?) zero as well.¹

I was hoping I might do better because, unlike them, I also know how to fix it, at least in the long term. But I still don't know how to get through to an individual. It literally doesn't matter how I put it, all they hear is "blah-blah-blah". If it's a text, it gets scrambled in their minds.

BTW, if anyone is wondering WTF am I talking about... Have you seen/read "The Minority Report"? Philosophy101 here asked for your help with the very Math that specialized mutated humans, called "Precogs", were doing to predict crimes before they happen.

And he didn't even try to hide what it is for -- which is getting a fucking AI to decide, formally or otherwise, whether you, should it come to that, will have your day in court, or be dismissed as insane.

And he sure got what he asked!.. So, again... what are we gonna do now?

 

¹ Or Jesus -- tho in his case, I'm much less certain that saving humanity was his primary goal till the end. Perhaps not from the start, but he knew what he is up against. So maybe he decided, instead, to, at least, help the only person that mattered most to him. To settle his debt. And that too was an impossible feat to pull -- but Jesus did it, and that's why he's amazing.