[tunesmith]

I've been reading about bayesian stats and likelihood ratios lately.

So, a likelihood ratio is P(X|A) / P(X|~A) .

If you define X as "likely to commit gun violence", then A would be the way to identify X.

Here, he's saying that A="plays violent video games". The problem is that not only is there a poorly correlated relationship between gun violence and video games, there's also plenty of gun violence by people who don't play violent video games. So the likelihood ratio isn't great.

It's the same with "is mentally ill". Even if you screen for mental illness, you're going to get a lot of false positives and false negatives.

The problem is that people keep trying to identify "A", and I suspect there isn't even a root cause. To me it seems like it's more a matter of multiple contributory causes that reach tipping points. System dynamics, if you will. For instance, if you reduce the allure of "preparing for the end of the world", that could have a system-level impact. Or, if guns looked feminine, that would probably do it too.

[stephengillie]

Is mentally ill doesn't have binary outcomes. Mental issues are set on spectrums (spectra?), usually from normal to extreme or extremely low to extremely high, normal in middle, and each human has an analog value on each spectrum for each disorder. With the latter, we expect a Poisson distribution.

[_delirium]

A particularly tricky aspect for the purposes of this discussion is that the positions on those spectra are somewhat circularly defined when looking at outcomes, at least as defined in the DSM, the most common U.S. diagnostic manual. Many of the conditions have outcome-related diagnostic factors right in the definitions: whether the person is experiencing significant distress in their life, conflict with others or their surroundings, inability to work a job, etc. The pragmatic goal is to avoid over-diagnosing things that aren't actually causing people problems, but as a result it's tricky to isolate causal factors. Even worse if you're diagnosing people in retrospect: of course someone who went on a shooting rampage is going to meet all those criteria, after the fact.

[tunesmith]

Well, yes - I meant it as shorthand for passing a screening test, since that is what they all talk about. Passing a screening test for mental illness will have a lot of false positives, and a lot of false negatives.

"Mentally ill" is one of those mysterious designations, anyway. No one really knows what it means. Is there a set of symptoms such that if you have them, you're definitely mentally ill, and if you don't, you definitely aren't?