Hello all,(adsbygoogle = window.adsbygoogle || []).push({});

I wonder if anybody knows of a way of generating a random normal vector (i.e. a variate from a multivariate normal distribituion) in which one or more of the vector's values are fixed?. For example, I may want to choose a random vector from a four-dimensional multivariate normal distribution constrained such that the second element of the random vector is equal to 0.1 and the third element is equal to 0.3; so I just want to pick values for the first and last element subject to these constraints).

In order to generate a completely random vector I have been using the method described on the http://en.wikipedia.org/wiki/Multivariate_normal_distribution#Drawing_values_from_the_distribution", that is, obtaining the dot product of the cholesky decomposition of the covariance matrix of the distribution and a vector of independent standard normal variates. I gather there may be a way of reverse engineering this, and working out what values in the vector "Z" are necessary to obtain the desired constrained output. But I can't find a way to do it!

I'd very much appreciate any help or suggestions.

Best wishes,

Mockle

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# Generating multivariate normal vectors under constraints

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