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In a comment on this question, the user 'probabilityislogic' says "No, not MCMC this thing! Quadrature this thing! only 2 parameters - quadrature is the "gold standard" for small dimensional posteriors, both for time and accuracy".

However I haven't been able to anything describing how to draw random variables using quadrature. How does one do it?

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    $\begingroup$ "Quadrature" is an old fashioned word for "compute an integral." This suggests a situation in which a posterior density is known, thereby permitting the probability of any event to be found by quadrature as well as opening the way to all kinds of algorithms to draw random values from the distribution. Since MCMC can itself be used for quadrature, the comment likely is referring to either analytical or definite (deterministic) numerical quadrature. $\endgroup$
    – whuber
    Apr 20, 2023 at 22:10
  • $\begingroup$ Thanks @whuber. Could you recommend a good reference for 'all kinds of algorithms'? I just know the inverse transform algorithm. $\endgroup$
    – Wilbur
    Apr 21, 2023 at 6:25
  • $\begingroup$ I am not aware of a single textbook or monograph covering all analytical and numerical procedures, but there are encyclopedic references that include some of this material, such as the Johnson & Kotz series on distributions. You might also review the technical help pages for statistical software, such as R, Stata, or SAS, where often references to their methods of random number generation from various distributions are given. $\endgroup$
    – whuber
    Apr 21, 2023 at 13:07

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