Is frequency or Bayesian interpretation used in quantum mechanics? In quantum mechanics, we deal with probability. There are two kinds of interpretations: frequency and Bayesian. Which one is actually used in quantum mechanics? My impression is, it doesn't matter. 
However, I would like to know if my understanding is correct. (I am not sure if this is opinion-based question)
 A: According to Jaynes, the different interpretations of probability do matter in QM. Not in terms of experimental outcomes, as the formalism gives the same predictions regardless of interpretation, but on how to interpret some  "paradoxical" situations. 
But the interesting point made by Jaynes is that Bell , because the way he interprets probabilities,  made a mistake in his inequalities' theorem  when he wrote the conditional probabilities. The right way to do it, according to Jaynes, is using bayesian rules, which results in a slightly different form for the equations that Bell's uses (see p. 11 of the article in the link). The result, according to Jaynes, is that Bell, left out an entire class of hidden variable theories because of its restricted point of view. I am not aware if Jaynes arguments have been debunked, though.   
A: Jaynes himself went a long way in applying rational Bayesian probability to classical statistical mechanics and (through his very interesting reappraisal of the theory of quantum mechanical mixed states) to quantum statistical mechanics also (see http://bayes.wustl.edu/etj/articles/theory.2.pdf).
But in regard to the problem of overcoming the interpretational problems of the quantum mechanics of pure states, Jaynes did not make much progress. And I think the reason for this lay partly in the form of the rational Bayesian probability theory he championed. This was essentially the logical theory of probability in which probability of a proposition is plausibility of that particular proposition given the truth of certain other propositions. Although he referred to these other propositions as representing (actual or supposed) knowledge (of the reasoner), Jaynes did not give much consideration to the fact that acquisition of that knowledge might affect the probability of the particular proposition on account of the uncertainty principle. Since we expect this to be so, we should, I think, switch to a more subjective approach to probability - to a Bayesian approach that sees the probability of a proposition as our degree of belief in the truth of that proposition given our knowledge. This is different whenever the uncertainty principle is active (i.e. of significance), because making a probability conditional on our knowledge means acquisition of that knowledge is taken as having happened, so the probability is not just contingent on certain propositions (the knowledge of the truth of which we acquired) but also on the process of acquisition by which we discovered those truths. We should therefore no longer refer to probabilities on condition certain propositions are true, but on condition we know them to be true. This alone resolves some of the interpretational problems of quantum mechanics.
Take a simple example. In the double slit experiment we cannot now speak of the probability for the particle to arrive somewhere on the screen supposing it passed through a particular slit. So the contradiction that this approach leads to (i.e. the absence of interference) is avoided. We can speak of the probability for the particle to arrive somewhere on the screen knowing it passed through a particular slit. But then the absence of interference of probabilities can be put down to our determination (by measurement) of which slit it passed through.
Another reason Jaynes did not make much progress in applying Bayesian methods to pure state quantum mechanics was that he stuck with the idea (pretty much generally accepted both then and now) that the wave function represents, at least in part, the physical state of the system. He did not, therefore view the wave function as a probability distribution, or as a probability amplitude (in Feynman's language). Tis held him back from developing a new theory of probability that would be consistent with the quantum mechanical formalism and in which the wave function would be a distribution representing our pure state of knowledge of a system (as the prominent physicist R F Peierls had already claimed it should; see http://iopscience.iop.org/article/10.1088/2058-7058/4/1/19/meta).
Why did Jaynes not want to experiment with a new theory of probability of this kind? Well, I suppose this was because he thought the nature of proper probability theory was already settled by Cox's derivation - that the ordinary sum and product rules of probability naturally followed from Cox's logical reasoning.
But Cox's derivation assumes probabilities to be represented by non-zero real numbers. If we assume they should be represented by complex numbers the situation is different.
Indeed, Saul Youssef has applied Cox's derivation without restricting probabilities to non-zero real numbers. He finds that complex-valued probabilities can satisfy Cox' axioms, and he is setting about deriving a new complex-valued probability theory for Bayesian reasoning in quantum mechanics, consistent with the usual quantum mechanical formalism. (He also thinks quaternions might well represent probabilities in the case of Dirac's relativistic quantum theory.) See http://xxx.lanl.gov/abs/hep-th/0110253
I, myself, am trying to develop a complex-valued probability theory for non-relativistic quantum mechanics and have self-published much work on this. (See the publication in my LinkedIn profile.) My approach is based more on Feynman's probability amplitude theory and not on Cox's axioms. It includes extensions of Jaynes' methods for calculating prior probabilities (principle of indifference, maximum entropy, method of transformation groups). These take a slightly different form because the probabilities are complex - the phases have to be taken into account as well as the amplitudes, but they can be usefully applied to help reproduce at least some of the findings of the usual quantum mechanical formalism, including the transformation functions and the Schrodinger equation. The complex-valued Bayesian probability theory (like classical Bayesian theory) demonstratively leads to definite expected frequencies of measured outcomes in repeated experiments designed to test quantum mechanics, so there is an (all important) connection with frequency even though probabilities are not themselves frequencies. The probability theory is applied to a realist picture of nature in which properties of systems (particle positions, momenta, spins, etc.) are real properties possessed by those systems having definite (if unknown) values at any time. Spooky action at a distance need not be present and contradictions from Bell-type inequalities and Kochen-Specker theorems are avoided.
