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Throughout my undergrad, I dreaded probability. I hated it, I was horrible in it, I just never got it, and felt stupid when the professors used "summation/marginalization" equations out of the blue to get rid of variables here and there. I just didn't understand it.

When I started my Masters degree, I was dreading that one Statistics/Prob course that I have to take, but then I was introduced to our lord and savior Bayes, and to be specific, Bayesian Networks.

It suddenly all made sense, all these equations that I suffered with, they were mostly variable eliminations on special Bayes Networks. Everything started clicking so much and by the end of the course I was dying to take more prob/stats.

So my questions boils down to, why isn't Bayesian Networks and Variable elimination introduced in undergraduate courses? I've looked at the vast majority of undergrad stat/probability courses in the top 10 us universities and none of them come close to explaining it, even though I feel it makes probability a whole lot easier and understandable!

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    $\begingroup$ I always felt prob/stat was pretty intuitive as is. Maybe your hurdle (and the fix for it) are not common. After all you are generalizing from a sample size of 1. $\endgroup$ – guest Apr 15 '18 at 13:21
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    $\begingroup$ It's worth noting that you found it intuitive as a grad student after taking a probability course. Would it be the same if you switched the order? $\endgroup$ – Adam Apr 15 '18 at 19:58
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    $\begingroup$ This may be a "monads are burritos" (byorgey.wordpress.com/2009/01/12/…) thing - attributing understanding a concept to the last idea that made it fit into place, rather than the years of struggle that were needed to be ready for that last idea. $\endgroup$ – Henry Towsner Apr 16 '18 at 3:27
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    $\begingroup$ @HenryTowsner Post it as an answer so I can +1 it :) $\endgroup$ – Chris Cunningham Apr 16 '18 at 12:37
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    $\begingroup$ As long as you are generalizing from a sample of size 1, A couple of years ago I experimented with using the book "Doing Bayesian Data Analysis" by Krunschke for a Mathematical Statistics course rather than the sort of traditional probability/stats course that I usually use. While the experiment was a partial success, the students still struggled as much as ever and didn't walk around with glowing light bulbs over their heads. $\endgroup$ – John Coleman Apr 16 '18 at 12:49
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(Expanded from my comment.)

The short answer is: because monads aren't burritos. That's a reference to this article, which I highly recommend.

We've all had the experience of getting one new perspective that makes a previously mysterious subject suddenly click into place, and it's tempting to credit the understanding to that idea and to be frustrated that no one explained it so clearly before.

In fact, often it was really all the work and thinking that went into trying to understand the subject before that prepared us to understand the topic; when that's the case, getting the great explanation earlier wouldn't have led to a breakthrough - it would have been another seemingly unhelpful explanation (which actually secretly made progress towards understanding) - and some later idea would have led to the breakthrough.

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    $\begingroup$ Good points. I also think there is a tendency for people to think that math should be learned in a linear manner. But in some cases, you just have to "get used to" certain abstractions and then learn the even more abstract justifications later. Humans are not computers. (Wikipedia articles are awful in this nature of explaining things with rigorous definitions rather than helpful explanations (with links to the more rigorous justifications...you end up in an incredible recursion tree, when you just wanted to understand what this particular "animal in the zoo" (math concept) was. $\endgroup$ – guest Apr 17 '18 at 23:23

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