Seeing Theory: A Visual Introduction to Probability and Statistics • Hacker News Board

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

#91

Post by Eugeleo » Thu, Oct 01, 2020, 10:27 AM UTC

qsort wrote: post #41

Eugeleo wrote: post #33

Earlier quoted context omitted.

I’ll copy my comment from other place in this thread, because I think it might be relevant here. I feel that most math subjects are treated either as full-on “fluff” (e.g. calculus, all computing, no theory building) or full-on theory (real analysis). A combination of intuition AND rigor is hard to come by. With that said... What textbook(s?) would you recommend for a thorough self-learning of statistics? I’m looking…

> I feel that most math subjects are treated either as full-on “fluff” (e.g. calculus, all computing, no theory building) or full-on theory (real analysis) My background is computer science and I had a similar experience. Just a caveat: I'm not arguing that we should stop teaching theory, quite the contrary: most of the times we err on the side of the fluff. In particular, the fact that many reputable institutions ar…

By the way, it seems that statlect focuses a lot on probability and so has quite an overlap with Feller. If you had to choose a primary text you'd read, which one of those two would you take?

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

#92

Post by cgriswald » Thu, Oct 01, 2020, 9:30 PM UTC

debbiedowner wrote: post #77

st1x7 wrote: post #54

Earlier quoted context omitted.

I see this argument a lot and for some reason it doesn't help me with the intuition at all. If you (wrongly) get caught up on the fact that the remaining door and your pick have the same initial probabilities of being a car, then you'll still think that switching doesn't make a difference even in the million-door case. Here's what works for me: - the switching strategy always gives you the opposite of your initial ch…

When Monty opens doors he uses 2 pieces of information: the door you picked and the correct door. After he opens 999,998 doors he has given you quite a bit of information. There is a 1/1000000 chance though that he has given you no information (you picked the correct door) But you're right that thinking about it in partitions also makes sense. You try to pick a partition size 1 that contains the prize, while Monty pi…

I think the point a lot of people miss is that the trick to understanding the 3-door question and the 1000000-door question is the same trick. If you don't grok the trick, the 1000000-door example might make it easier to grok, but there's a fair chance it won't.

To muddy the waters further, it's not always understood that in the 1000000-door case, 999998 other doors are opened (as evidenced by discussion elsewhere in these threads). Sometimes people think it's still just one door. I suspect this is because the original problem is usually stated as "...Monty Hall then opens one of the doors you didn't pick" and because people suggesting the 1000000-door often just say "...what if there were one million doors?"

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

#93

Post by cgriswald » Thu, Oct 01, 2020, 9:58 PM UTC

jibal wrote: post #48

will_pseudonym wrote: post #28

Earlier quoted context omitted.

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?

But this raises a different problem with intuition: If Monty doesn't know where the car is, then if 999,998 doors were opened showing goats, leaving two doors, the odds that the car is behind your door or behind the remaining door is 1:1 ... this defies many people's intuition. The difference between the two cases is that, if Monty knows where the car is, then his opening 999,998 doors with goats behind them is exact…

My intuition is that:

1) I will probably lose when Monty opens a car door. 2) If I don't, I am really gambling between whether I made a 1-in-a-million pick or Monty did (in the choice of which door to leave shut), which obviously has even odds.

Interestingly, by compressing this problem back down to the 3-door version, it makes it pretty obvious why that's the case (and aligns with people's intuition about the original problem). Also interesting that in this case, even if the intuition is wrong (that 'obviously' they must have picked the car), the outcome (sticking with the chosen door) is an optimal strategy.

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

#94

Post by unwaryquerier » Sat, Oct 03, 2020, 1:34 AM UTC

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…

"The law of Small Numbers" chapter 10?