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Why isn't this random number generation implemented?

Posted 8 years ago
POSTED BY: Chi-Hsiang Wang
6 Replies

Yes, I found a lack of robust MCMC in Mathematica is surprising, and disappointing, too! In the last couple decades full Bayesian analysis has become fairly popular and MCMC is at present one of the most powerful methods to obtain any posterior distributions. In fact my need was to obtain a simulated posterior distribution that involves logistic functions and beta distributions, both of which are basic functions/distributions for categorical data analysis.

Hope Wolfram ups its efforts in improving robust functional capabilities for statistical data analysis, particularly Bayesian data analysis!

POSTED BY: Chi-Hsiang Wang
POSTED BY: Sjoerd Smit
POSTED BY: Szabolcs Horvát

Many thanks, Sjoerd and Marco. So it seems, as Sjoerd suggested, Wolfram hasn't implemented multivariate random number generation for user-defined distributions. It's certainly possible to use conditional probability for simulation, but let's hope Wolfram provide handy, automatic functions like RandomVariate for this purpose very soon.

POSTED BY: Chi-Hsiang Wang

In the special case described in the original post, this one should generate the points:

RandomPoint[Disk[], 10]

Cheers,

Marco

POSTED BY: Marco Thiel

I'm guessing that this is because sampling from arbitrary multi-dimensional distributions is generally not a simple problem which they haven't got around to implement yet. There are some trivial exceptions like ProbabilityDistribution[1, {x, 0, 1}, {y, 0, 1}], but in general it seems like you can only use build-in multi-dimensional distributions with RandomVariate.

In your case, you could try to sample the unit disk by transforming the coordinates to r and theta. This will factorize the distribution so you can draw from two 1D distributions, which should be easy to do.

POSTED BY: Sjoerd Smit
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