Quantum Bayesian Networks

October 3, 2014

First Ever Photo of Majorana Fugitive

Filed under: Uncategorized — rrtucci @ 4:55 am

The Majorana Fermion (alias The Major) has been sought by police authorities for more than 75 years; in fact, since 1937, when his daddy, Ettore Majorana, first reveal his existence to the world. And now, finally, that elusive fugitive has been captured, and put into a bound state, or prison cell. Detectives were able to lure him into an iron wire, and then cornered him at the end of that wire. It is believed that in such a bound state, The Major will lose his anti-social fermion behavior and start behaving more gregariously, like an anyon. Here is a mugshot of The Major, while in his prison cell:
anyon-selfie
This rainbow-colored picture is meant to convey, respectfully, the fact that The Major is LGBT (he is neither a fermion nor a boson, but something gay in between). Leon Lederman calls him The Gay Particle.

For a police report describing the events that led to The Major’s capture, see

http://phys.org/news/2014-10-majorana-fermion-physicists-elusive-particle.html

And here is a Wikipedia profile of this most wanted fugitive:

http://en.wikipedia.org/wiki/Majorana_fermion

So what will come next? A quantum computer composed of millions of gay particles? The conservatives are horrified at this prospect, and have vowed to do everything in their power to oppose the building of such an abomination, a gay quantum computer, something which is explicitly forbidden by the Bible.

References

October 1, 2014

Monty Hall Problem, as discussed by a 5 year old Illuminati

Filed under: Uncategorized — rrtucci @ 9:52 pm

A friend just sent me a link to the following NYT article:

The Odds, Continually Updated by Flim D. Flam (would I lie to you?) Sept. 29, 2014, New York Times

Even though the article doesn’t mention the obvious fact that quantum computers will someday soon revolutionize the Bayesian field (because they will be able to do Bayesian calculations much faster than classical computers), it’s not such a hopelessly outdated, clueless piece of reporting. Really. The article doth sing the praises of Bayesian techniques, so it ain’t that utterly bad.

The article makes a big deal about the Monty Hall problem. It’s a cute problem, for a five years old. Correction: A five year old that has been taught Bayesian networks. We B net advocates teach our children Monty Hall on day one, of pre-kindergarten. It’s quite conceivable that an intelligent 50 year old kid who has been taught only the frequentist canon might spend hours on such a problem, and ultimately give up.

Here is how a 5 year old illuminati who is conversant with the language of B nets would discuss such a piddling problem:

Let \theta({\cal S}) stand for the “truth function”. It equals 1 if statement {\cal S} is true and 0 otherwise. For example, \theta(a=b)=\delta_a^b is the Kronecker delta function.
monty

The Monty Hall problem can be modelled by the B net shown, where

c= the door behind which the car actually is.
y= the door opened by you (the contestant), on your first selection.
m= the door opened by Monty (game host)

If we label the doors 1,2,3, then m,c,y\in \{1,2,3\} and

P(c)=\frac{1}{3}

P(y)=\frac{1}{3}

P(m|c,y)=\frac{1}{2}\theta(m\neq c)\theta(y=c)\;\;\;+\;\;\;\theta(m\neq y,c)\theta(y\neq c)

It’s easy to show that the above node probabilities imply that

P(c=1|m=2,y=1)=\frac{1}{3}

P(c=3|m=2,y=1)=\frac{2}{3}

So you are twice as likely to win if you switch your final selection to be the door which is neither your first choice nor Monty’s choice.

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