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Part of my project requires that I do some sampling and although I can find some answers, i find my questions to be rather basic ( like sampling from a truncated normal or sampling from a marginal distribution). I could find answers here, but I feel that it should be easy to find an answer to such questions in a book, but it seems that there is no such thing. I can't find any theory properly written!

My question is, can I find such a book/ pdf lecture, and if yes, where :)?

Edit: Some context to better understand my question:

A couple days ago, I wondered how to sample from a marginal distribution $f_X(x) = \int f(x|y) f(y) dy$, I asked around, got an answer, but they weren't able to explain why it worked ( sample from y plug y in the conditional, keep the x) , and it sort of makes sense but i can't justify it, and it happened to me before that when it comes to sampling, no one can give much more than recipes. And i would like to know where i can find how to "prove" it.

Thank you :)

kjetil b halvorsen
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Max C
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    It's not really clear to me what specifically you are interested in. Are you interested in [inverse transform sampling](https://stats.stackexchange.com/q/307686/1352)? Or in software implementations? Can you please clarify? – Stephan Kolassa Oct 16 '17 at 07:54
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    Ok, well, couple days ago, I wondered how to sample from a marginal distribution $f_X(x) = \int f(x|y)f(y)dy$, I asked around, got an answer, but they weren't able to explain why it worked ( sample from y plug y in the conditional, keep the x) , and it sort of makes sense but i can't justify it, and it happened to me before that when it comes to sampling, no one can give much more than recipes. And i would like to know where i can find how to "prove" it. Thank you :) – Max C Oct 16 '17 at 08:05
  • Thanks! Could you please edit that information into the question? That would make it a lot easier to answer. (And comments are ephemeral.) – Stephan Kolassa Oct 16 '17 at 08:20
  • I have edited my question – Max C Oct 16 '17 at 08:28
  • A good book is "Simulation" from Sheldon Ross. Chapters 3, 4 and 5 explain all about generating random numbers. – StijnDeVuyst Oct 16 '17 at 09:15
  • Linked: but unanswered... https://math.stackexchange.com/questions/1700315/do-sample-from-and-insert-parameter-commute – Fabian Werner Nov 26 '18 at 16:41
  • I think my answer here will help u to get the idea https://stats.stackexchange.com/questions/233581/mc-sampling-from-a-posterior-distribution/233750#233750 – Bahgat Nassour Nov 30 '18 at 11:22

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