2
$\begingroup$

I'm learning Monte-Carlo approach in sampling. There I faced with ways of how to draw samples from given distribution. But can you give me an example of a distribution which can not be trivially simulated as normal or binomial distribution?

| cite | improve this question | | | | |
$\endgroup$
  • 4
    $\begingroup$ It's still not quite clear what your last sentence is asking. Do you mean "cannot be as trivially simulated as normal or binomial"? What's your trivial means of simulating a binomial? What makes something trivial or non-trivial more generally? $\endgroup$ – Glen_b -Reinstate Monica Jun 2 '15 at 10:46
  • $\begingroup$ von Mises-Fisher is also such an example, cf. this previous post on Cross Validated. $\endgroup$ – mic Jun 18 '15 at 12:39
5
$\begingroup$

Drawing gamma random numbers usually requires rejection sampling, it is less trivial.

I assume that you refer to trivial if the CDF is invertible, or conversion from the uniform to the target distribution can be resolved with thresholds.

| cite | improve this answer | | | | |
$\endgroup$
4
$\begingroup$

In this earlier Cross Validated question, a density defined as $$h_β(r)∝(1−w_{\mu,τ}(r))f_{β_0}(r)+w_{\mu,τ}(r)g_{ϵ,σ}(r)$$ is proposed, with a non-trivial simulation solution.

In my class, I usually give the benchmark density target $$h(x)\propto \{1+\sin^2(2x)+\sin^4(4x)\}\exp\{-x(1+\cos^2(4x)+\cos^4(2x))\}$$ to simulate. You can make similar examples by piling up complex but upper bounded terms.

| cite | improve this answer | | | | |
$\endgroup$

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.