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.