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An excerpt from a technical explanation...
One of the things I'm trying to do is get my mind wrapped around Bayesian inference and hypothesis testing[1]. I found a site which gives both an "intuitive" and a "technical" explanation of Bayesian reasoning.

I was delighted to find, in the midst of the technical explanation, the following passage (on technical explanations):
Too many academics think that being "technical" means speaking in dry polysyllabisms. Here's a "technical" explanation of technical explanation:

The equations of probability theory favor hypotheses that strongly predict the exact observed data. Strong models boldly concentrate their probability density into precise outcomes, making them falsifiable if the data hits elsewhere, and giving them tremendous likelihood advantages over models less bold, less precise. Verbal explanation runs on psychological evaluation of unconserved post facto compatibility instead of conserved ante facto probability density. And verbal explanation does not paint sharply detailed pictures, implying a smooth likelihood distribution in the vicinity of the data.

Is this satisfactory? No. Hear the impressive and weighty sentences, resounding with the dull thud of expertise. See the hapless students, writing those sentences on a sheet of paper. Even after the listeners hear the ritual words, they can perform no calculations. You know the math, so the words are meaningful. You can perform the calculations after hearing the impressive words, just as you could have done before. But what of one who did not see any calculations performed? What new skills have they gained from that "technical" lecture, save the ability to recite fascinating words?

"Bayesian" sure is a fascinating word, isn't it? Let's get it out of our systems: Bayes Bayes Bayes Bayes Bayes Bayes Bayes Bayes Bayes...

The sacred syllable is meaningless, except insofar as it tells someone to apply math. Therefore the one who hears must already know the math.

Conversely, if you know the math, you can be as silly as you like, and still technical.

[1] Bayesian inference is a method of evaluating the likelyhood of hypotheses based on evidence received. If, for example, you feel that there's a 20% chance your son would steal your wallet if he's using drugs, and your wallet isn't stolen, how should that affect your belief that your son's using drugs (hint: there's not quite enough information to answer the question).