One of the pioneers who developed popular instructional materials for teaching Quantum Mechanics is N. David Mermin of Cornell University.
A proper mathematical understanding of the calculus of QM requires a graduate level appreciation of probability and statistics − especially the concepts of statistical correlation, Bayesian Inference, and the conscientious application of Bayes Rule.
Since many physics students do not have this prerequisite, Mermin devised a simplified shortcut to finesse this gap. His shortcut relies on a construction somewhat akin to the famous Monty Hall Problem.
In Mermin's construction, he invites his students to contemplate a pair of statistically correlated boxes with three buttons and a light bulb that turns either red or green, depending on how the buttons are pushed.
Feynman had independently devised a similar analogy, but Mermin's version proved to be simpler to present and reckon.
Not unlike the notorious Monty Hall Problem, Mermin's scenario reveals just how hard it is to wrap one's brains around even simple problems calling for a careful application of the calculus of Bayesian Inference.
There is an even trickier aspect in Mermin's Two-Box Scenario in that the act of pushing a button (akin to opening a door in the Monty Hall Problem) disturbs the state of the arrangement of the stuff inside the box. In the Monty Hall Problem, opening one door does not cause the items behind the other two doors to trade places. But in Mermin's scenario, sometimes (one time in four), pushing a button does cause a behind-the-scenes switcheroo. So if you thought the Monty Hall Problem was mind-boggling, Mermin's Two-Box Three-Button scenario is even more insidious.
And yet, both problems are tractable within the scope of the somewhat arcane mathematics of statistical correlation and Bayesian Inference. Indeed, the innards of Mermin's boxes could be modeled as a Semi-Markoff Process. That's the good news. The bad news is that a graduate level course in Markov Processes is even more rarefied and arcane than a graduate level course in Probability and Statistics.
Mermin is now retired, but he recently surfaced to praise a new approach to Quantum Mechanics known as QBism (Quantum Bayesianism). In a sense, QBism isn't really new. Einstein, Bohr, Schroedinger, and Heisenberg were perfectly competent in the arcane mathematics of probability, statistics, correlation, and the calculus of Bayesian Inference.
Mermin is famously quoted (especially by Feynman) as saying, "Shut up and calculate." The calculation (surprise, surprise) is the application of Bayes Rule to the QM scenario at hand. The idea is that trying to mentally model the underlying Semi-Markov Process is simply too mind-boggling if you haven't taken (and mastered) a couple of semesters of graduate level courses in Probability, Statistics, and Markov Models.
And so, with the advent of QBism, Mermin has enthusiastically endorsed it as a cleaner introduction to the Bayesian Calculus than his confusing Mermin Boxes. Both Mermin and Feynman had relied on the pedagogy of the Mermin Boxes, only to discover that their students remained just as muddled as mainstream physicists had been for the past 70 years trying to understand the meaning of the mathematics of QM.
Here is David Mermin's recent article in Nature
...Physics: QBism Puts the Scientist Back into Science
by N. David Merminhttp://www.nature.com/news/physics-qbism-puts-the-scientist-back-into-science-1.14912
See also the accompanying editorial ...Be Here Nowhttp://www.nature.com/news/be-here-now-1.14922
QBism challenges the student to appreciate (if not master) the good old-fashioned mathematics of Probability, Statistics, Correlation, and Bayesian Inference.
And with that, the muddle-headed woo-woo of QM disappears like a Boojum, an imaginary critter that never was.