A couple of years ago I was just learning Python and was playing around with matplotlib. Running simulation of a dice roll 100, 1000, 10,000, 100,000, and 1,000,000 times started to show how the distribution starts to catch up with the expected 1/6th probability of each face. I was thinking how good it would be to teach young students this way.
On a different thread this morning someone bemoaned the lack of statistical education - a sentiment that is widespread among people who have studied and worked with statistics and probability. It is really exciting to see pedagogical tools that help explain basic but important concepts like distributions and sampling. Great work.
What textbook(s?) would you recommend for a thorough self-learning of statistics? I’m looking for both intuition _and_ mathematical rigor — not all proofs, but not all fluff either.
I’m a bioinformatics student and I will have a semester of combined probability/stats some time this year, but I think that won’t be enough to support me given my preference for DS-based bioinformatics jobs.
I’m reading Feller right now for the probability stuff, but I’m unsure about statistics. I don’t even know what the relation between probability and statistics is — most similar questions I found online (i.e. “How to learn stats?”) are answered with a “Read this probability book and you’re good”.
So so cool ! And it goes to show how poorly probabilities and statistics are usually taught, it's such a waste. I'm working on a non profit project aiming in parts to aggregate this kind of pedagogical tools into a collaborative learning map and serving it in a personalised way: https://sci-map.org. Early phases still, but if people are interested to contribute please hit me up!
"If you roll 2 six-sided dice, what are the chances you roll at least one dice above 5 (5 or 6)?"
A nice trick to visually solve this in your head I heard once is:
If you think of rolling two dice as a square. X and Y are each dice. You get a 36 square board. Getting 1 six is just the upper boarder. 6 on the top, 6 on the right (6 and 6 overlap). So 11 out of the 36 squares.
This looks brilliant. This can be very useful to grasp the concepts of probability and statistics in a visual way. I've been struggling to understand some of the concepts and I hope to use this as a supplement. Although, I don't believe it can replace a university course or a proper text book.
How come that an undergraduate person (at the time) makes one of the most compelling statistic textbooks?
Is it because there are many more amateur statistic textbooks in existence, or published attempts at one (so more chance for a runaway success to be picked up)?
Or is it because people in the statistic textbook industry don't feel this frustration and/or don't dare to take any risk?
nice use of interactive data visualization to explain concepts, would love to see more teachers use this approach.
I must say that this website/way of reading a book is simply gorgeous
Brain does not count. It updates/alters its structures - the process which humans model with numbers and back propagation.
Numbers do not exist outside of human cultures.
Got stuck at chapter 2 since there was zero indication what a valid syntax for a set was.
What a beautiful study resource.
This is a really cool website!
Very interesting and helpful !
Amazing. Thanks for sharing!
Gorgeous web design
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"Don't trust your intuition". This should be the basis for all teaching in statistics and probability. If all goes wrong, it should be the one thing everyone remembers from their statistics education. And yet year after year, everyone is starting with E(X)=sum(x*P(x)) and has no idea what it was about afterwards.
With calculus and linear algebra your gut feel is about right no average. You can quickly get a feel for trajectories, acceleration and distances (derivatives and integrals), areas, volumes, amounts, etc. But on probability your gut-feel will always fool you.
In the end, you see a handful of math bloggers bemoaning the lack of education in probability and the nonsense being discussed by journalists and politicians. And it hardly matters whether it's an election or a pandemic. The lack of understanding of uncertainty and the false belief that one can reason about these without looking at the numbers too closely is dangerous.
Sorry about the rant. But...
Dear creator of seeing-theory.brown.edu, if there is one thing you could change about the project to make it different and infinitely more useful: Please start the first chapter with the goat problem[1], then go through a couple of examples from chapter 10 in Thinking Fast and Slow[2], the discuss information (maybe with a simplified version of Mendel's pea experiment[3]), discuss distributions and leave expectations and variances for much-much later.
[1]: https://en.wikipedia.org/wiki/Monty_Hall_problem [2]: https://en.wikipedia.org/wiki/Thinking,_Fast_and_Slow [3]: https://www.sciencelearn.org.nz/resources/1999-mendel-s-expe...