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RobertLumley comments on Casey Anthony - analyzing evidence using Bayes - Less Wrong
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Comments (19)
Thanks for posting this.
I don't know about Bayes but I think Occam's razor (simplest explanation for the data) indicates that most likely she's guilty of murder. Here are the relevant events (as evidence) that I'm thinking about:
Casey Anthony borrowed a shovel from her neighbor on June 18th 2008. Cayley Anthony was last seen alive on June 15th 2008.
There were search queries like chloroform, 'how to break a neck' (and others) found on Casey Anthony's computer - through reconstructed Firefox cache browser. The computer files were deleted to hide the data, so special software was used to reconstruct the data.
There was a month between the last time Cayley Anthony was seen alive and the time she was reported as missing. When she was reported as missing, it was the grandmother, Casey Anthony's mother Cindy Anthony, who reported it.
I could go on and on and on...
The jurors acquitted Casey Anthony on the basis that there was no connection between her and the dead body of the child and that prosecutors weren't able to prove a link between her and the dead body of the child.
My reaction is that if you look at all the circumstantial evidence, the simplest explanation that fits all the data is that she probably killed her child. Yes, you can have someone just curious about chloroform searching google. Yes, it may also have been food rotting in the car. Yes, Casey Anthony may have borrowed the shovel for gardening - but if you string together all these explanations, the final conjunction of all of them just becomes a lot less probable.
The things that need to be distinguished are "guilty" and "committed murder". "Not guilty" and "innocent" are very, very different terms. I haven't met anyone who thinks she didn't commit the murder, but A. was there enough evidence to prove it, and B. Did the prosecution actually prove it? Maybe, and absolutely not.
The other thing that's bothered me as of late about a purely Bayesian approach is this: I'm reading Elizer's OB posts in order from the beginning, and I'm almost to 2008. Perhaps he addresses it at some point, but he hasn't yet in my reading. (I've also read the intuitive explanation, but having had three separate statistics classes, Bayes was a subject I understood pretty well to begin with.)
Shouldn't there be some accounting of the standard deviation of your estimate of your priors? If I have a prior that I've reached by amounting ten bits of evidence, that is quite different from a prior that I've reached by amounting one bit of evidence. I don't see how a traditionally Bayesian approach takes this into account.
(And sorry that's somewhat off topic, it's just bothered me for awhile now.)
Check out Metauncertainty. The post Joys of Conjugate Priors gives a specific example.
That post should be linked to more often. It is fundamental for discussions of calibration. It should have been promoted, frankly.
Thanks, I'll read those when I get a chance.
What exactly do people mean by 'proof'? With near certainty, almost nothing can be proven.
Since the body decomposed under the soil for 30 days, it's really hard to determine the precise case of death - even though I think some prosecution witnesses made the argument that it was a homicide. It's hard to link the murderer with the body, since the body was discovered so much later.
I think the prosecution had enough 'circumstantial evidence' to get a conviction. I think that beyond a reasonable doubt, Casey Anthony was responsible for the child's death. It may not have been murder but something happened to that child which this woman tried to cover up.
I know that the law works under the presumption of innocence but I wonder why prosecution was assumed to be under such burden of proof. Doesn't the defense also have a burden to explain the duct tape, the stench, etc.? Has the defense met that burden? I don't think so.
"Doesn't the defense also have a burden to explain the duct tape, the stench, etc.? Has the defense met that burden?"
In law, there is no such burden. It doesn't matter. The only thing the defense must prove is that the prosecution failed to prove their case. And 12 jurors who spent far more time in the courtroom than either you or I agreed that they did not. And did so quite quickly, as jury deliberations go. But the prosecution had no murder weapon, so solid motive, and no time of death. From what I've read (which is admittedly limited) they even did a poor job with cause of death.