I must say that this website/way of reading a book is simply gorgeous
Seeing Theory: A Visual Introduction to Probability and Statistics
61–70 of 94 posts
Re: Seeing Theory: A Visual Introduction to Probability and Statistics
#62How 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?
Re: Seeing Theory: A Visual Introduction to Probability and Statistics
#63Earlier quoted context omitted.
Many people have suggested this "intuitive" explanation. But it's not at all clear or intuitive that jumping from 3 to 1,000,000 doors should lead the host to open 999,998 other doors rather than 1 other door.
"But it's not at all clear or intuitive that jumping from 3 to 1,000,000 doors should lead the host to open 999,998 other doors rather than 1 other door." It SHOULD be clear, because you have two givens: 1) Monty never reveals the car. 2) He opens all the doors except 1.
"2) He opens all the doors except 1"
How is this a given exactly? In the original problem he only opens 1 other door. Now that also happens to be all doors except 1, but from just the 3 door problem that seems more coincidental than a fundamental part to the question
Re: Seeing Theory: A Visual Introduction to Probability and Statistics
#64This 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.
Re: Seeing Theory: A Visual Introduction to Probability and Statistics
#65"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?
What gave me the intuition for it was to realise that Monty is giving you the choice to either stick with your original door, or take the sum of the prizes between the other two doors.
(He also opens one of those two doors to reveal a goat, but you already knew that one of them had a goat so that doesn't give you any additional information.)
Re: Seeing Theory: A Visual Introduction to Probability and Statistics
#66What 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 f…
Rather than a textbook, I've had success getting a copy of the course notes directly from the stats department. The best textbooks I've read where history of statistics and philosophy of statistics. > I’m reading Feller right now for the probability stuff, but I’m unsure about statistics. Probability is the study of mathematical objects, and nobody is totally sure if any of them exist even in the approximate. Is anyt…
Probability Theory is a branch of mathematics. Statistics is the art of processing data to extract information suitable for the human cognitive system or a computer algorithm. Statistics use mathematical tools like physics or chemistry do.
Re: Seeing Theory: A Visual Introduction to Probability and Statistics
#67What 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 f…
I cannot recommended them because I have them on my back burner, but I would like to start working through the "Think" Stats series soon [1].
I love the premise: "if you know how to program, you can use that skill to learn other topics."
Perhaps someone here can speak to their experience with some of these books?
Re: Seeing Theory: A Visual Introduction to Probability and Statistics
#68Earlier quoted context omitted.
"Once you develop intuition, probability is really quite intuitive" That's a tautology. Plenty of studies, such as the work by Kahneman and Tversky, show that humans by default have incorrect statistical intuitions. These faulty intuitions are hard to overcome, even by a considerable amount of training. > The Monte Hall problem is more of a curiosity than a fundamental principle! It's quite straightforward conditiona…
> It's quite straightforward ... No it is not, unless it is explicitly stated that Monty knows where the car is and that he deliberately opens a door with a goat. Just look at the discussions in the comment here.
> unless it is explicitly stated that Monty knows where the car is and that he deliberately opens a door with a goat.
That has been part of the explicit problem ever since it was first presented back in 1975.
"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?"
Re: Seeing Theory: A Visual Introduction to Probability and Statistics
#69"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 mathematics behind probability and statistics is about as ripe for intuition as calculus and linear algebra. A lot of it really comes down to counting in probability (calculus/measure theory for the continuous case) and quantifying properties about probability distributions for statistics. The really hard part is the modelling part, where you transform the problem to a mathematical statement and vice versa. It's…
It's because math courses are crazy expensive and teaching both modelling and theory together would mean taking way longer (read costing way more) or making the failure rate (cost) way higher.
Re: Seeing Theory: A Visual Introduction to Probability and Statistics
#70What 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 f…
Not a text, but I highly recommend the Bland and Altman Statistics Notes in the BMJ. They are usually 1 page, easy to read explanation on a single statistic topic.
Here is one on the Odds Ratio for example https://www.bmj.com/content/bmj/320/7247/1468.1.full.pdf