Can anyone recommend a specific type of statistics course?
I would like to find a good Statistics course to do for myself, and also to recommend to others, down the road ... one that specifically focuses on risk, and the discrepancy between actual statistical probability vs humans' intuitive sense of risk.
I recall a quote, which The Interwebs informs me right now, came from Albert A. Bartlett ... "The Greatest Shortcoming of the Human Race Is Man’s Inability To Understand the Exponential Function".
Alternately, Mark Twain popularized (but did not originate) the saying "There are lies, damned lies, and statistics".
That's the kind of course I'm looking for, that focuses on questions like how much should we actually worry about supervolcanoes, asteroid strikes, Covid 2.0, WWIII, Trump getting re-elected, etc.
There are two parts to this. One, people often (naturally, human nature, how our brains are wired to handle Risk) obsess about a short list of risks in life that are overblown, or appear to be more of a concern than they actually are.
The other part is, some things have a very small risk of actually happening, but when considered in conjunction with the potential consequences (asteroid strikes, WWIII, global pandemic), are still worthy of aggressive efforts to prevent ... and people often focus on the first element (statistically unlikely) and dismiss or overlook the second piece (devastating consequences).
Anyway, stuff like that ... ideally an actual, hands-on MOOC-type Statistics course, but even a good youtube video or blog article would suffice.
As usual, thanks in advance.
At least to my layman's ears it sounds like you might actually be looking for something more akin to a psychology course on cognitive biases and decision-making, rather than a statistics one.
As for where to find something like that, I have found Coursera to be a pretty good place to start looking. And IMO this Behavioral Finance course from Duke University actually seems to match your criteria reasonably well despite its financial focus.
Edit: These sociology/international affairs courses, Global Systemic Risk (from Princeton) and Risk in Modern Society (from Leiden), may also interest you too.
I am also looking at/for such things, yes ... but that's another day. Right now, I am definitely interested in the math and statistics of accurately assessing risk and probability, but in a context that looks at "accurate results" as opposed to our natural preconceptions.
The course you linked does sound good and I may try it out. I am quite interested in things like that, and eg Freakonomics, Thinking, Fast and Slow, etc ... all good stuff, but yeah, right now, I literally want to learn more about the math involved in accurately assessing these things, rather than "just" pointing out human thinking defects.
If that's the case then it sounds like you're actually just looking for some basic statistics courses, which are pretty easy to find. But if you want to get even more specific then Actuarial Science might be another related discipline that you might want to look into, since probabilistic mathematical modeling of risk and uncertainty is its main focus. I am not aware of any freely available courses for that though since it's a highly specialized, cross-disciplinary field.
Perhaps you're interested in Bayesian statistics more generally? The central tenant of Bayesian statistics is that you must incorporate your priors when making predictions (i.e., use Bayes's theorem).
Here's the typical example, explained in a few different sources (ordered from least to most math):
More specifically, it sounds like you're interested in decision theory (try googling "introduction to decision theory risk"). As a lay starting point, you might consider the work of Eliezer Yudkowsky, e.g. "Cognitive Biases Potentially Affecting Judgment of Global Risks". (Although this recommendation comes with the caveat that his personal framework, which he calls "timeless decision theory", might only be half-baked ).
Eliezer is the guy that finally managed to explain Bayes Theorum in a way I understood (although I see now he actually recommends another person's explanation as even better ... just found my morning reading). Also, his Harry Potter fan fiction should be required reading in primary schools. I really wanted to love his old Less Wrong site, but it's just weird.
Mathematics usually isn’t contextualized like this, just take a basic stats course. Have you done any calculus classes?
Calc and statistics, both, but too many decades ago to remember anything. Time for a do-over.
Make sure you have a thorough understanding of integration, understanding statistics will be much easier.
I'll echo others in that I don't think many, if any, stats courses would focus on that. You're looking for gaining an intuition of statistics, but a) that's mostly gained through experience working in statistics b) intuition in the end is not anything initofitself within the field - it's a means to an end so you can work towards using more rigorous proofs and techniques to prove your conclusion.
If you want to gain a intuition of probability, honestly I think Poker is a great way if you play at least semi-seriously. There's few opportunities where you quite literally get to roll the dice and observe the results thousands of times a session. Trump winning in 2016 was about the odds per 538 of a flush draw on the river - as a Poker player, the pot odds on a flush draw are usually enough to bet for. So a Poker player would never eschew that chance, even if many people interpreted it as 0%.
Thanks ... if such a course doesn't exist, I may just have to (re-)learn statistics well enough to make that course, because it really should exist.
I took statistics in ... high school, or first year of college (wow, I can't even remember that ... imagine how much I remember from the actual class). At the time, I was into D&D (still am), and I was endlessly fascinated by the statistical probabilities of the results of rolling 4d6, discarding the lowest number and adding up the other three. The chance of rolling either a 3 or an 18 is simple to calculate, but it gets tricky in the middle.
I was already writing (simple) computer programs in the early '80s to simulate those dice rolls thousands of times to generate the probabilities empirically...
Daniel Kahneman and Amos Tversky have some interesting (and highly decorated) work on cognitive biases related to risk. I’m not sure that’s exactly what you’re looking for because it’s not a stats course, but the subject of cognitive biases seems to me what you’re asking about. The subject of behavioral economics has a lot on this topic as well, and experimental economists (many of them influenced by Kahneman and Tversky) have done some interesting work to build up empirical data.
Yeah, I actually just referenced him in my previous response. I love his book Thinking, Fast and Slow.
Good point. That is a great book!
You might want to look at 'extreme value' theory/statistics/analysis.
https://en.m.wikipedia.org/wiki/Extreme_value_theory