Let’s eat, Grandma!

vs.

Let’s eat Grandma!

From a naive perspective, the result they show is cumulative, some sort of weighted sum of the answers so far. The questions aren’t independent, and some answers are far more determinative than others, so looked at that way the weights must be dependent on the answers. But that’s probably not the best way to look at it. Kind of like the latest vaccine kerfuffle, where the original analysis used conditional logistic regression, and the (incorrect) reanalysis used a naive Pearson’s chi-squared that takes no account of confounders.

wrt different modeling assumptions, one place different costs of errors might be introduced is in how likely a juror is to influence other jurors.

Also, one picky point–I believe the NYT talked to jury selection consultants, who often are social scientists or other specialties, not lawyers. So, whatever your prior is about lawyers not understanding statistics should have limited weight over jury selection specialists.

]]>So I think the error here is in the way the questions are phrased. It would be more precise to say something like: “The initial estimate is based on the assumption that you are employed and make more than $50K (and so on for the other questions). If you tell me different, I will update my beliefs accordingly. But if you confirm my assumption, that has no effect.”

So that’s my attempt to give everyone involved the benefit of the doubt. However, there is another oddity you didn’t mention, Ted. The text suggests that lawyers are updating probabilities differently depending on whether they represent the plaintiff or the defendant.

The only way I can make _that_ rational is if lawyers make different modeling assumptions, depending on who they represent, and therefore compute different odds ratios. And I suppose their modeling choices could be justified by different costs for different kinds of errors.

]]>By the way, does this have anything to do with Mr. T recently having been de-selected for jury duty?

There are other serious problems with lawyers not understanding probability, such as the prosecutor’s fallacy.

]]>I also complained about the wrong location of Hanover on a map; it was way too far to the west. Since I’ve seen this several times, it is probably a case of one mistake being copied several times. (Map makers do introduce deliberate mistakes into maps, usually small dead-end streets which do not exist, so that they can easily prove copyright infringement. On a similar note, after a referee noted a typo in Eq. 50 or whatever, I thought it might be a good idea to deliberately insert one in order to check how diligent the referee was.)

]]>I completely agree with Jeff Huffman. This device definitely would violate conservation of energy. More generally, you can’t break momentum conservation without also breaking energy conservation.

I don’t think I understand Oona Houlihan’s suggestion. Unless the “something” that’s pulled in already has lots of momentum in the direction the ship is going, I don’t see how this helps.

]]>I’ve read numerous blogs about this, and so many of them seem to say something along the lines of “this isn’t as crazy as violating conservation of energy – it’s not a perpetual motion machine.” Of course, violating momentum conservation is just as crazy. But if this “device” actually worked, couldn’t one easily use it to create a perpetual motion machine (of the first kind)? Classically, the total input energy is Pt (P = power in), and the kinetic energy of the device is proportional to t^2. So at some point you’re getting out more energy than you’re putting in.

Or am I missing something?

]]>Either way, in quantum mechanics they tell you the couplings between angular momentum states. They answer questions like this: If you have a system with a certain amount of spin angular momentum and a certain amount of orbital angular momentum, what are the possible values of the total angular momentum, and what are the probability amplitudes for each?

I need them for things that have nothing to do with quantum mechanics. It turns out that they are also (up to boring constants and the like) the answer to this question: what do you get when you integrate the product of three spherical harmonics over the entire sphere? For one reason or another, I needed to incorporate such integrals into something I was calculating.

Update: the person who replied to my bug report initially denied there was a problem, but when I explained it again, more clearly this time, he agreed. It’s been sent on to the relevant coders, presumably to be fixed in the next version.

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