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st: Simulate from a random process


From   Chris Wallace <c.wallace@qmul.ac.uk>
To   statalist <statalist@hsphsun2.harvard.edu>
Subject   st: Simulate from a random process
Date   Fri, 28 May 2004 13:26:50 +0100

I need to simulate from a random process and am not sure how to go
about it.  The process is the probability of an event occuring between
a pair of points on a line. (This probability is between 0 and 0.5).

I have estimates of these probabilities for a series of points, their
standard errors and the correlation matrix (which is AR(1)).  Eg (for
4 points)

             estimated prob (q):   0.1163  0.1280  0.0698

                 standard error:   0.0320  0.0288  0.0259

  asymptotic correlation matrix:   1.0000
                                  -0.0880  1.0000
                                   0.0000 -0.0739  1.0000

The vector q is used in a further analysis, treated as known.  I would
like to simulate alternative vectors q, which could be used in the
further analysis in order to generate some empirical confidence
interval.  But I don't know where to start with such simulation.  (In
practice, q has about 50 elements).

Although I know how to use cholesky decomposition to simulate
dependent variables from a MVN distribution, I am stuck on two counts
here:
- the distribution for q
- how to incorporate the dependence into the simulation.

I would appreciate any suggestions.

Chris.


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