Has Jaynes's argument against Bell's theorem been debunked? As a student of theoretical physics I'm well acquainted with the multitude of crackpot ideas attempting to circumvent Bell's theorem regarding local hidden variable theories in quantum physics. 
Recently, however, I've been working on my master's thesis regarding Bayesian probability, and I came across a very interesting paper by Jaynes on precisely the subject of Bell's theorem (E.T. Jaynes, Clearing Up Mysteries - The Original Goal, In: Proceedings, Maximum Entropy and Bayesian Method, 1989).
Jaynes writes about what he calls the Mind Projection Fallacy and its prevalence in quantum mechanics. He claims the fallacy is a result of failing to appreciate probabilities as representations of states of knowledge (epistemological), as opposed to as fundamental properties of nature (ontological); clearly, Jaynes advocates the Bayesian perspective on probability.
Using his 'Bayesian inference as extended logic' approach, Jaynes derives a number of - to me - impressive results in this paper and others. More to the point, on pages 7-16 he explains two objections to Bell's results:


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*Bell didn't appreciate the difference between the epistemological nature of probability in making predictions and the ontological nature of causality. This lead him to propose the wrong probability distribution for his class of hidden variable theories; one which is indeed (trivially) violated by quantum mechanics.

*Bell did not include all local hidden variable theories. For instance, his choice excludes those where the hidden variables are time-dependent.
These objections don't read crackpot in my opinion, and as demonstrated in the linked papers there is a slight historic tendency for the Bayesian perspective to make one see old results in a new light, particularly in other fields of physics.
I've heard that Jaynes is adept at making himself seem obviously right and others obviously wrong - so I may have fallen for that trap - but this argument struck me as something that should've gotten a lot more attention than I'm aware it has. That is, I was still taught the Copenhagen interpretation complete with Bell's theorem ruling out local determinism, which seems to imply that this argument has either not gotten mainstream attention or has been thoroughly debunked.
Are there any obvious counters to Jaynes' viewpoint that I'm not aware of?
 A: Bell's argument actually fails in a deterministic universe. The argument's fundamental assumption is that the outcome of a measurement on one particle can't depend on the measurement basis chosen by the other experimenter for the other particle at a spacelike separated location. This is usually described as a locality assumption, but there's more to it than that. If the experimenter's choice is actually an inevitable consequence of the state of the universe at earlier times, then it's possible that it's an inevitable consequence of the state at the place and time that the entangled pair of particles was created. If so, the particles could decide then and there how to respond to the measurements that inevitably will happen later, reproducing the prediction of quantum mechanics without any spooky long-distance communication.
It's hard to imagine how elementary particles could know in advance the result of a physical process as complicated as the choice of a measurement basis by an experimenter, nor how that choice could be predictable solely from information localized in a small part of its past light cone, and as far as I know no one has actually proposed a local hidden variable theory in which this happens. But Bell didn't prove it impossible.
So if Jaynes is taking the hardline position that the universe is deterministic and all probabilities are inherently about our lack of knowledge of its state, I think he's at least morally correct, and he may be literally correct in his entire argument. He's right that Bell's argument assumes a Y-causes-X relationship in the probabilities P(X|Y), and he's right that there is no such relationship in subjective probabilities. You need some kind of objective unpredictability in the world for Bell's argument to go through – not quantum unpredictability, but some sort of free choice or true classical randomness at the spacelike separated locations of the measurements.
To the extent that Jaynes acts like the mystery of Bell's theorem is totally resolved just because he can model the quantum prediction in his classical probabilistic logic, I think he's wrong. A deterministic model where particles know the future is not logically impossible, but it would be really frickin' weird, and I don't expect any such model to appear. (Although, quantum mechanics is also weird, and I never would have predicted it, so I suppose I should expect to be surprised.)
A: I'm a fan of Jaynes and doubt that there is a legitimate refutation to his objection of the lack of time variance, though I think that should obviously be extended to space-time.
The natural conditioned variables for deterministic events in space-time for something with a spacetime wavefunction would have to include the space-time of each event, detector orientation, and any quantum interactions of the measurement devices themselves. Maybe the last doesn't play much of a part, but for a deterministic theory, the rest are obvious.
M1(d1| st0, st1, or1, lambda(st0))
M2(d2| st0, st2, or2, lambda(st0))
You would detect/not detect based on OR1 alignment relative to particle state at st1 after it's split at st0 and state lambda(st0).
Jaynes' objection is straightforward. Bell didn't analyze conditioned on these other parameters, hence did not rule out a hidden variable theory based on them.
The problem with any "there is no such theory that" is that it has to assume some class of theories. If Bell didn't condition on the space-time of each event, then he didn't. If others didn't, then they didn't.
Also, mathematics advances. You can't cover all possible mathematics. We expand the use of mathematical structures as we find an effective use of them. Saw some paper mentioning imaginary valued probabilities. What does that mean? Who the hell knows? But I bet Bell didn't include imaginary probabilities in his class of possible solutions to analyze for a deterministic theory.
From the description in the blog post, the Gill paper seems a convoluted special case, introducing "free choice" analysis confusing matters and besides the point, and less likely to produce a valid probabilistic analysis than Bell's original scenario.
I wish there was a source of raw data of detector counts from which we could attempt to construct a deterministic theory.
A: Bell was simply wrong, did not understand basic probability math, and the experiments actually show no difference between all the ideas and  Einstein–Podolsky–Rosen's (EPR) simple hidden variable.  Remember Occam's, and please choose the simpler explanation.
The math is explained properly by Jaynes, but I'll make it very simple with an example.
Two particles are created such that they have opposing spins. This is a given, but we will gloss over the fact that the spins are not necessarily exactly opposite at every point in time in their futures. We only require that some physical measurement (e.g. angular momentum) is conserved according to what current theory or measurement says so. But let's for the moment assume they are always opposite.
If we assume EPR, then there is some 3D vector showing the spin poles of each particle.  We don't know what it is yet, so we measure it.  (By the way, this is identical to what would happen with quantum mechanics (QM), that the actual value only exists at measurement time.)  But how?  We have this apparatus that shows if some set angle of a piece of equipment is aligned with the spin of the particle.  Well, not exactly, as we could never get it aligned exactly, so our apparatus just tells us if the angles are off by less than 90 (spin UP) or more than 90 (spin DOWN) from the the angle we chose.  So our unknown value, as measured in the 2D plane of our rotating test, can only tell us that the actual spin value of particle A was somewhere $\pm$ 90 degrees to our test angle. This is the same regardless of EPR or QM. The actual value, whether it collapsed just now, or existed from $t_0$, we can only know the value was in this half of the potential solution space.
Now we know with certainty that the other particle B must be in the other 180 degree part of the circle.  If the other measurement was 90 degrees off from the first, we would expect 50/50 chance of UP or DOWN, as the known 180 degree possible area is divided exactly in half.  If the chosen angles were the same, there is 100% chance they will be opposite. However, if measurement B was 120 degrees off from A, there is a smaller possibility they will have the same result! We are simply revealing the underlying real physical value. The expositions of the form, "look at these 9 possible outcomes of 11, 12, 13, 21, etc" do not correctly describe that each of these 9 buckets have different probabilities as a function of how we are measuring, and what angles we choose.  The 5/9ths ratio is false!
And now that I have shown you how easy it is to see with an example, you should use the correct math equations as Jayne does.  The expected outcome of measurement B changes when we have information from measurement A. No need to separate with a long distance. No transfer of state.  Just a little more info gained.
And it makes no difference!  These experiments can never reveal what is really going on.  We can only know that there is a fuzzy value of some measurement that tells us which half of a circle had the spin of the thing when we measured it.
I like Occam; no nonsense required.
A: This sounds more like a mild crackpot, the further I read. He accuses Bohr of assuming that all instruments are subject to the uncertainty principle (fourth paragraph, page 8).  This, however, was an experimental observation, not an assumption.
Page 9, end of paragraph 2, he accuses Bohr of confusing limitations on QM theory with limitations on the validity of lab measurements. This is a rather dubious point, as theory is needed to interpret experimental results.
Further on page 9, 5th paragraph, he essentially refutes the orthodox QM view by defining it as incorrect, stating that it violates his "necesarry division of labor" in theoretical physics.
At the top of page 13, the author makes a distinction between a physical influence faster than light and a logical inference, which is charactaristic of the intangibility of the "spooky action at a distance". It does not, however, change the result of the reasoning of the EPR experiment.
The last part, where it looks like he's getting into a possible loophole, he mentions time-varying hidden variables, but really doesn't say clearly how this would work.  His closing statement sums his views up well.
It is very common for crackpots to object to relativity or quantum mechanics on "philosophical" grounds, (which I put in quotes to avoid insulting philosophers) and treat their own philosophy as axiomatic. This seems to be what he's doing.
