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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.
During that month, Casey Anthony was seen as partying and entering 'hot-body' contests.
In Cindy Anthony's call to 911, she describes the stench in Casey Anthony's car as a foul smell 'as if someone died in there'.
The body was found only a quarter a mile away from the house where here parents and Casey Anthony live.
There was a duct tape with the skeletal remains of the body. Same type of duct tape was also found in Anthony household.

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.

AlexMennen14y00

Sounds like Casey is overwhelmingly likely to be guilty. It also sounds plausible, but unlikely (and maybe more evidence makes it less likely; this post is all I've read on the matter), than Cindy killed Cayley.

2RobertLumley14y

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.)

2

Casey Anthony - analyzing evidence using Bayes

by Zachary_Kurtz

7th Jul 2011

1 min read

2

I'm just curious if anyone has weighed the evidence from the Casey Anthony murder using a Bayesian filter. Someone made a very useful post like this for the Amanda Knox case, but I think for this case it would be even more useful. Given the apparent hysteria in traditional media, social networks, etc. it would be great to have a nice dose of rationality about the case.

My gut feeling is that most people have not bothered to weight the evidence, but look at the surface layers of the case and judge based on questionable heuristics. It also seems to me that the members of the jury had a lot more time and reason to carefully weigh the evidence (even if they aren't Bayesians) than your average, angry twitter user. Additionally, coming out on one side or another gives a great opportunity to signal (think of the children vs. strict constitutionalism).

Any thoughts?

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[-]Jonathan_Graehl14y70

Most people haven't weighed the evidence for the same reason I'm not motivated to do so - there's nothing in it for me. It helps that none of my friends talk about the case.

As well, I don't see any obvious way to attack it with Bayesian tools. (As Hamming reminds us in "You and Your Research"*, what makes a problem important is not what consequences solving it would have (like FTL or antigravity) but whether you have any productive lines of attack on it. What questions have the highest marginal return?)

The only consideration I can think of even close to the insightfulness of komponisto's analysis of how the coverup is the only hard question in the Knox case would be to ask how often mothers cover up a murder of their children they were not culpable in. And when you ask it like that, then Anthony looks highly likely to be guilty.

* Serendipitously, I just learned there's apparently an expanded book form available online

[-]komponisto14y20

The only consideration I can think of even close to the insightfulness of komponisto's analysis of how the coverup is the only hard question in the Knox case

Naturally, I greatly appreciate the compliment and the link. (Thanks!) However, I have to point out that this isn't a correct summary of that post. A correct summary would be: "the burden of proof for demostrating a coverup by Knox and Sollecito is as high as for demonstrating their guilt of murder". I don't claim that the question of whether there was a coverup is particularly hard to resolve (to the contrary, the aforementioned claim implies strongly that there almost certainly wasn't a coverup), and nor do I compare its difficulty with other aspects of the case.

ask how often mothers cover up a murder of their children they were not culpable in

As I understand it, the principal defense theory in the Anthony case is that it wasn't a homicide at all, but an accident that was covered up.

The line I was thinking of was the one about how hard work has to be done somewhere, and if the coverup implied guilt, then the work had to be done on the coverup. But OK, thanks for the correction.

The only consideration I can think of even close to the insightfulness of komponisto's analysis of how the coverup is the only hard question in the Knox case would be to ask how often mothers cover up a murder of their children they were not culpable in. And when you ask it like that, then Anthony looks highly likely to be guilty.

This morning I read the following. I still don't have statistics on this but this should be relevant:

Nicholson, who worked as a social worker on the child abuse team at Dayton Children’s before becoming director of Care House in 1998, said there are facts about the case that she finds extremely troubling. “What I can tell you definitively is that the parents of children who die accidentally don’t lie about it; they don’t wait 31 days before reporting the deaths, and those are facts of this case that are seemingly indisputable,” Nicholson said.

That doesn't really tell us much - lying about accidents is rare, OK. Parents murdering their children, accidentally or deliberately, are also pretty rare. It's the ratio of rarity which tells us which to prefer in lieu of any other evidence - which is rarer?

[-]komponisto14y40

Someone made a very useful post like this for the Amanda Knox case

Link. ;-)

My gut feeling is that most people have not bothered to weight the evidence, but look at the surface layers of the case and judge based on questionable heuristics.

Indeed. My own more specific theory is that people -- this includes juries, by the way -- judge these cases by first sizing up the defendant's personality and deciding how much they sympathize with him or her (in almost all cases, the answer is "very little"), deriving a prior for guilt directly from that, and then looking at other evidence in the case to see whether it confirms this initial impression. This theory accounts nicely for the otherwise perplexing emphasis that people put on psychological evidence such as the defendant's "lies", both in the Knox case (where this negative impression is based on misinformation and misunderstanding) and in the Anthony case (where the defendant does appear to have behaved in an authentically unsympathetic fashion).

FWIW, my take on the case is that (from what I know from very limited media exposure) there is a substantial probability that Anthony is guilty of murder, well over 10%, possibly over 50%, but very likely well below the 99% or so that I would consider "beyond reasonable doubt". In this, the case is sharply distinguished from that of Knox, where in my view the hypothesis of guilt lacks sufficient evidence even to be considered.

[-]AnlamK14y-10

komponisto, I would be very interested in reading if you decided to do a similar post (to the Knox case post you had) for this case as well - even if it's just a discussion post.

Also, you say that p(Anthony=guilty) is 'possibly over %50'. Let's assume it's %50.

This claim could be interpreted as the following. Suppose that there are X many possible scenarios for what happened, given the constraints of our evidence about the case. In X/2 Anthony is guilty and in X/2, she is not guilty.

This seems implausible to me. X/2 alternate scenarios (scenarios that don't involve Anthony's guilt) seem too many.

What other alternate scenarios are there?

[-]Sophronius13y20

Judging from what I read on wikipedia:

-She is clearly guilty of child neglect, making her more likely to be guilty of either murder or manslaughter

-The body is too far gone to see how the child died, and there are no witnesses or convincing dna evidence

-Overall, there is very little evidence that points in favour of either murder or manslaughter to the exclusion of the other

-Manslaughter has a higher prior probability than murder (especially when swimming pools are involved, which are responsible for about 25% of all deaths for children that age from what I've read)

-Therefore I find that probability (manslaughter or other cause) > probability (murder)

-Legally speaking, she can not be convicted of murder beyond reasonable doubt

-however, the probability of her being guilty of murder is still around 20%

-Legally speaking, she can not be convicted of manslaughter beyond reasonable doubt

-however, the probability of her being guilty of manslaughter is still around 65%

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.
During that month, Casey Anthony was seen as partying and entering 'hot-body' contests.
In Cindy Anthony's call to 911, she describes the stench in Casey Anthony's car as a foul smell 'as if someone died in there'.
The body was found only a quarter a mile away from the house where here parents and Casey Anthony live.
There was a duct tape with the skeletal remains of the body. Same type of duct tape was also found in Anthony household.

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.

[-]RobertLumley14y20

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.)

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.

Check out Metauncertainty. The post Joys of Conjugate Priors gives a specific example.

[-]komponisto14y30

Check out Metauncertainty.

That post should be linked to more often. It is fundamental for discussions of calibration. It should have been promoted, frankly.

[-]RobertLumley14y10

Thanks, I'll read those when I get a chance.

[-]AnlamK14y-20

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.

[-]RobertLumley14y00

"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.

[-]AlexMennen14y00

Sounds like Casey is overwhelmingly likely to be guilty. It also sounds plausible, but unlikely (and maybe more evidence makes it less likely; this post is all I've read on the matter), than Cindy killed Cayley.

If you (or anyone else) are still interested, I recommend this article . I think I'm pretty close to the position the author articulates.

Let me note that most (all?) of this evidence is contested by the defense. Juror #3 Jennifer Ford, in her post-verdict interview with ABC news, said that she didn't believe the evidence based on chloroform.

The stench similarly was also contested.

I personally think that Case Anthony at least caused the death of Cayley that involved criminal elements. So, I am biased - I've made up my mind. I could change it if someone could explain all of the above in a more plausible way.

Judging by the public uproar, I guess that most people think she is guilty. Even the jurors themselves said that they 'were sick to their stomachs' in delivering the verdict, which is a strange display of human psychology.

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