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    <p>The rank correlation method of <a href="http://www.informaworld.com/index/780064783.pdf" rel="noreferrer">Iman and Conover</a> seems to be a widely used and general approach to producing correlated monte carlo samples for computer based experiments, sensitivity analysis etc. Unfortunately I have only just come across this and don't have access to the PDF so don't know how the authors <em>actually</em> implement their method, but you could follow this up.</p> <p>Their method is more general because each variable can come from a different distribution unlike the multivariate normal of @Dirk's answer.</p> <p><strong>Update:</strong> I found an R implementation of the above approach in package <a href="http://cran.r-project.org/web/packages/mc2d/index.html" rel="noreferrer"><code>mc2d</code></a>, in particular you want the <a href="http://finzi.psych.upenn.edu/R/library/mc2d/html/cornode.html" rel="noreferrer"><code>cornode()</code></a> function.</p> <p>Here is an example taken from <code>?cornode</code></p> <pre><code>&gt; require(mc2d) &gt; x1 &lt;- rnorm(1000) &gt; x2 &lt;- rnorm(1000) &gt; x3 &lt;- rnorm(1000) &gt; mat &lt;- cbind(x1, x2, x3) &gt; ## Target &gt; (corr &lt;- matrix(c(1, 0.5, 0.2, 0.5, 1, 0.2, 0.2, 0.2, 1), ncol=3)) [,1] [,2] [,3] [1,] 1.0 0.5 0.2 [2,] 0.5 1.0 0.2 [3,] 0.2 0.2 1.0 &gt; ## Before &gt; cor(mat, method="spearman") x1 x2 x3 x1 1.00000000 0.01218894 -0.02203357 x2 0.01218894 1.00000000 0.02298695 x3 -0.02203357 0.02298695 1.00000000 &gt; matc &lt;- cornode(mat, target=corr, result=TRUE) Spearman Rank Correlation Post Function x1 x2 x3 x1 1.0000000 0.4515535 0.1739153 x2 0.4515535 1.0000000 0.1646381 x3 0.1739153 0.1646381 1.0000000 </code></pre> <p>The rank correlations in <code>matc</code> are now very close to the target correlations of <code>corr</code>.</p> <p>The idea with this is that you draw the samples separately from the distribution for each variable, and then use the Iman &amp; Connover approach to make the samples (as close) to the target correlations as possible. </p>
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    1. POUsing R to honor correlations for LatinHypercube / Monte Carlo trials
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    1. USGavin Simpson
    1. USGavin Simpson
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    1. CONice answer, Gavin, to an under-specified question as we were never told whether this was just multivariate Normal (or t or ...), or, as you surmise, something a little cleverer.
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      1. USDirk Eddelbuettel
    2. CO@Dirk Thanks - my initial inclination was to respond as you did with the `mvrnorm()` but you beat me to that one and then I wondered about this rank correlation method I had been reading about.
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      1. USGavin Simpson
    3. COThank you very much.. The cornode function does the trick! I was trying really hard to find a similar function in python
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