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Seeing Theory: A Visual Introduction to Probability and Statistics

seeing-theory.brown.edu

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Re: Seeing Theory: A Visual Introduction to Probability and Statistics

#21

Post by whatever1 »

jtsuken wrote: post #14

"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…

We are very good at finding correlations. It is still very hard to prove causality in natural phenomena from experiments, specially when we cannot control them. This became blatantly obvious in the covid outbreak where nobody had a clue for months about whether masks would help or not. Edit to clarify: It is very hard to prove to causality and be sure that you did not mess up.

Re: Seeing Theory: A Visual Introduction to Probability and Statistics

#22

Post by ivansavz »

Layvier wrote: post #19

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!

sci-map sounds very interesting. Have you looked at metacademy.org before? They did a lot of good work on the data model (concepts, resources, learning pathways, etc), and also collected a lot of content, mostly on computer topics. https://metacademy.org/graphs/concepts/bayesian_logistic_reg...

Sadly the project is no longer actively developed but if you haven't seen it yet, you should definitely check out for inspiration: https://github.com/metacademy

Re: Seeing Theory: A Visual Introduction to Probability and Statistics

#23

Post by Layvier »

ivansavz wrote: post #22
Layvier wrote: post #19

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!

sci-map sounds very interesting. Have you looked at metacademy.org before? They did a lot of good work on the data model (concepts, resources, learning pathways, etc), and also collected a lot of content, mostly on computer topics. https://metacademy.org/graphs/concepts/bayesian_logistic_reg... Sadly the project is no longer actively developed but if you haven't seen it yet, you should definitely check out for inspir…

I didn't know about, seems very similar indeed! I will check it out in details, thanks a lot for sharing !

Re: Seeing Theory: A Visual Introduction to Probability and Statistics

#24

Post by harshitaneja »

ArtWomb wrote: post #16
shekharshan wrote: post #8

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.

In an effort to reduce screen time, I recently tried to instigate a game of classic table-top Dungeons & Dragons. And I swear, kids were even more interested in the BigInt N-sided die function I cribbed in a python shell than any demons or demigods ;) Seeing Theory interactivity is very interesting. I think if there is one canonical example to tie it all together it would be something akin to "estimate the likelihood…

I had a similar idea to teach physics, well mostly scientific thinking and process by using a physics game engine for our world or some esoteric one and then asking them to perform some actions by creating theories of how the system behaves. Moving from a qualitative analysis of the system to building concrete quantitative theories and then in later stages having their simple theories fail as we deal with more complex interactions with the system and having them adapt their models of this world or rethink another.

Imagine how much their thought process would change if they intimately understood how scientific modelling works.

Re: Seeing Theory: A Visual Introduction to Probability and Statistics

#25

Post by will_pseudonym »

laddng wrote: post #11

"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.

Another way to think about it using the square board concept would be to figure out how many ways you can get not the result you're looking for, and take 36 minus that number for the number of possible squares out of 36 squares. So getting "no 6's" on either die would be the square on the board of 1 through 5, by 1 through 5, or 25 squares. So inverting that we'd arrive at the 11 squares.

In studying probability, I found that accounting for the "overlap" as you described it was more tedious in more complicated problems than just always calculating the joint probabilities and inverting them.

Re: Seeing Theory: A Visual Introduction to Probability and Statistics

#26

Post by wodenokoto »

jtsuken wrote: post #14

"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…

Why are you calling the Monty Hall problem for the goat problem?

It is known in academic circles as Monty hall and when it pops up in popular media, it is also referred to as Monty hall.

Re: Seeing Theory: A Visual Introduction to Probability and Statistics

#27

Post by will_pseudonym »

wodenokoto wrote: post #26
jtsuken wrote: post #14

"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…

Why are you calling the Monty Hall problem for the goat problem? It is known in academic circles as Monty hall and when it pops up in popular media, it is also referred to as Monty hall.

From Wikipedia[0]

... It became famous as a question from a reader's letter quoted in Marilyn vos Savant's "Ask Marilyn" column in Parade magazine in 1990 (vos Savant 1990a):

Suppose you're on a game show, and you're given the choice of three doors: Behind one door is a car; behind the others, goats. You pick a door, say No. 1, and the host, who knows what's behind the doors, opens another door, say No. 3, which has a goat. He then says to you, "Do you want to pick door No. 2?" Is it to your advantage to switch your choice?

[0] https://en.wikipedia.org/wiki/Monty_Hall_problem

Re: Seeing Theory: A Visual Introduction to Probability and Statistics

#28

Post by will_pseudonym »

jtsuken wrote: post #14

"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…

On the topic of the Monty Hall problem, what helped me "believe" it more was if you change it to 1,000,000 doors, still with only 1 car, and the rest goats. You choose 1 door. The host then opens up 999,998 other doors, which all contain goats. So there are 2 doors left. Your door, and the only other door the host didn't open. Do you feel at a gut level that you should switch?

Re: Seeing Theory: A Visual Introduction to Probability and Statistics

#29

Post by mturmon »

jtsuken wrote: post #14

"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…

Wow, strong disagree. Once you develop intuition, probability is really quite intuitive. This kind of course should be working to develop this intuition — like the conditional probability examples and the CLT examples. The computational examples inline really help here.

The Monte Hall problem is more of a curiosity than a fundamental principle!

(Was a TA in undergrad engineering probability for 2 years, saw my share of learners.)

Re: Seeing Theory: A Visual Introduction to Probability and Statistics

#30

Post by WildParser »

jtsuken wrote: post #14

"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…

My professor for statistics (he was quite famous in the field) talked about Monty Hall, but made clear that he will not give a solution because of science-political reasons.
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