You might be also be interested in "General Bayesian Theories and the Emergence of the Exclusivity Principle" by Chiribella et al. which claims that quantum theory is the most general theory which satisfies Bayesian consistency conditions.
By now, there are actually quite a few attempts to reconstruct quantum theory from more "reasonable" axioms besides Hardy's. You can track the refrences in the paper above to find some more of them.
As you learn more about most systems, the likelihood ratio should likely go down for each additional point of evidence.
I'd be interested to see the assumptions which go into this. As Stuart has pointed out, it's got to do with how correlated the evidence is. And for fat-tailed distributions we probably should expect to be surprised at a constant rate.
Note you can still get massive updates if B' is pretty independent of B. So if someone brings in camera footage of the crime, that has no connection with the previous witness's trustworthiness, and can throw the odds strongly in one direction or another (in equation, independence means that P(B'|H,B)/P(B'|¬H,B) = P(B'|H)/P(B'|¬H)).
Thanks, I think this is the crucial point for me. I was implicitly operating under the assumption that the evidence is uncorrelated which is of course not warranted in most cases.
So if we have already updated on a lot of evidence, it is often reasonable to expect that part of what future evidence can tell us is already included in these updates. I think I wouldn't say that the likelihood ratio is independent of the prior anymore. In most cases, they have a common dependency on past evidence.
From the article:
At this point, I think I am somewhat below Nate Silver’s 60% odds that the virus escaped from the lab, and put myself at about 40%, but I haven’t looked carefully and this probability is weakly held.
Quite off-topic: what does it mean from a Bayesian perspective to hold a probability weakly vs. confidently? Likelihood ratios for updating are independent of the prior so a weakly-held probability should update exactly as a confidently-held one. Is there a way to quantifiy the "strongness" with which one holds a probability?
Thanks for your answer. Part of the problem might have been that I wasn't that proficient with vim. When I reconfigured the clashing key bindings of the IDE I sometimes unknowingly overwrote a vim command which turned out to be useful later on. So I had to reconfigure numerous times which annoyed me so much that I abandoned the approach at the time.
A question for the people who use vim keybindings in IDEs: how do you deal with keybindings for IDE tasks which are not part of vim (like using the debugger, refactoring, code completion, etc.)? The last time I tried to use vim bindings in an IDE there were quite some overlaps with these so I found myself coming up with compromise systems which didn't work that well because they weren't coherent.
At least for me, I think the question of whether I'm buying too much for myself in a situation of limited supplies was more important for the decision than the fear of being perceived as weird. This depends of course on how limited the supplies actually were at the time of buying but I think it is generally important to distinguish between the shame because one might profit at the expense of others, and the "pure" weirdness of the action.
We have reason to believe that peptide vaccines will work particularly well here, because we're targeting a respiratory infection, and the peptide vaccine delivery mechanism targets respiratory tissue instead of blood.
Just a minor point: by delivery mechanism, are you talking about inserting the peptides through the nose à la RadVac? If I understand correctly, Werner Stöcker injects his peptide-based vaccine.
You could also turn around this question. If you find it somewhat plausible that that self-adjoint operators represent physical quantities, eigenvalues represent measurement outcomes and eigenvectors represent states associated with these outcomes (per the arguments I have given in my other post) one could picture a situation where systems hop from eigenvector to eigenvector through time. From this point of view, continuous evolution between states is the strange thing.
The paper by Hardy I cited in another answer to you tries to make QM as similar to a classical probabilistic framework as possible and the sole difference between his two frameworks is that there are continuous transformations between states in the quantum case. (But notice that he works in a finite-dimensional setting which doesn't easily permit important features of QM like the canonical commutation relations).
There are remaining open questions concerning quantum mechanics, certainly, but I don't really see any remaining open questions concerning the Everett interpretation.
“Valid” is a strong word, but other reasons I've seen include classical prejudice, historical prejudice, dogmatic falsificationism, etc.
Thanks for answering. I didn't find a better word but I think you understood me right.
So you basically think that the case is settled. I don't agree with this opinion.
I'm not convinced of the validity of the derivations of the Born rule (see IV.C.2 of this for some critcism in the literature). I also see valid philosophical reasons for preferring other interpretations (like quantum bayesianism aka QBism).
I don't have a strong opinion on what is the "correct" interpretation myself. I am much more interested in what they actually say, in their relationships, and in understanding why people hold them. After all, they are empirically indistinguishable.
Honestly, though, as I mention in the paper, my sense is that most big name physicists that you might have heard of (Hawking, Feynman, Gell-Mann, etc.) have expressed support for Everett, so it's really only more of a problem among your average physicist that probably just doesn't pay that much attention to interpretations of quantum mechanics.
There are other big name physicists who don't agree (Penrose, Weinberg) and I don't think you are right about Feynman (see "Feynman said that the concept of a "universal wave function" has serious conceptual difficulties." from here). Also in the actual quantum foundations research community, there's a great diversity of opinion regarding interpretations (see this poll).