[R] sampling randomly from general correlated multivariate PDFs

gnuman b.smith at irl.cri.nz
Wed Jul 22 00:22:26 CEST 2009


(apologies if this looks like a re-post, I just sent a similar message to the
r-help mail list.  This version is via Nabble.)
My intended application is error propagation using the ISO GUM Supplement 1
approach (propagation of distributions using Monte Carlo strategies).  To
automate uncertainty analysis I typically have the following data:
(1) a measurement function y(x1,x2,...xn)
(2) 'n' input variables (x1,x2,...xn) their means and covariances and
marginal PDF forms (I'm only contemplating using common PDFs like gaussian,
uniform, poisson, triangular, lognormal,...).
(3) degrees of freedom for each input quantity
then
we want to simulate draws from each of the xi (say 10000, so we get n*1000
random numbers) and correlate them as per the covariance data, without
destroying the form of the marginal PDF for each xi.

Q. I'd like to know if there are packages that can be used to efficiently
simulate such random
draws from general multivariate (joint) PDF functions when ONLY the
independent marginal PDFs
are known (RV means and covariance or correlation matrix)?

Q. I see there is a Markov Chain Monte Carlo package, but the mcmc
documentation is
not clear enough for me to be able to use it to simulate draws from joint
PDFs.  I'd like
to automate this type of task in R.  Is there another Monte Carlo strategy
that has
an R interface that can do this work?

I've read papers by Mishra (2004) and Al-Subaihi (2004) that give clues on
how to use MCMC, but 
I'm not adept enough (yet) to translate their strategies into a general
purpose R module. 
Surely this has already been done by someone?  Can anyone help?

Other Stats Questions/comments:
* I'm aware the underlying joint PDF cannot be uniquely determined, but I
assume for
certain simulation purposes sampling correlated RV's from the marginal PDFs
is
sufficient (eg., my purpose is uncertainty or error propagation, using say
the
ISO GUM Supplement 1 Monte Carlo approach).  Is this assumption correct, or
for
error propagation are there strong caveats to observe.
(ASIDE: The ISO GUM Supp.-1 does not provide advice on how to simulate RV's
drawn from
multivariate PDFS for other than the multivariate normal dist. for which I
can easily
use the mvtnorm or mnormt packages.)

Thanks in advance.
bms.
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