[kqr]

As much as I would like to, I think getting to that understanding required at least 500 flashcards on general statistical and probability concepts, ranging from fundamentals to extreme value theory. Most of those are only barely relevant at face value, but still contribute to understanding.

It's not that I set out to understand this specific thing but that I had studied statistics with flashcard support for a year and that happened to work after a few attempts.

[parmenidean]

Completely makes sense, appreciate the thoughtful reply. Any tips for writing flashcards when studying a textbook?

[kqr]

I've long wanted to write about this but never been able to think of anything original to say, but your question forced me to face this with effort. Thanks!

When making flashcards I draw a lot from the softer type of theory-building they do in social sciences. I ask questions like

- What are the properties of this?

- What variants of this exist? I.e. how would I recognise this in the wild, or in other shapes?

- What subcomponents can this be deconstructed into?

- Into which bigger picture does this fit?

- What are the consequences of this? What are its antecedents?

- What is this a special case of? What would a generalisation of this look like?

- Which are other related things? What are their similarities and differences?

- In what context might I need to know this?

Whenever I encounter what seems like a significant thing I loosely ask some of these questions, and try to construct atomic, focused flashcards from the answers.

I say loosely because it would take forever to to through all questions for all flashcards I make, so there's some bit of intuition that attracts me to which I think are the most significant questions for any given thing.

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One trick to make flashcards more specific that I use (maybe even abuse) is putting part of the answer into the prompt. Instead of prompting "What is the property of subexponential distributions I found meaningful in this book?" I might prompt "What behaviour do subexponential distributions have around high barriers that others don't?" -- I'm giving away part of the answer by including "high barrier" in the prompt, but I'm okay with that.

If I'm concerned about that, I might create a second flashcard prompting something like "What can a subexponential distribution do in one step that a more well-behaved distribution needs many steps to do?" with the answer "clear a high barrier". That captures both sides of the property without making too general a prompt.

I also do this a lot with "why" questions. Instead of prompting "what is the definition of y?" I might prompt "why is the definition of y=f(x)?" That gives away essentially the entire answer but focuses on the why instead.