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

**Physics Forums | Science Articles, Homework Help, Discussion**

Dismiss Notice

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Generating multivariate normal vectors under constraints

**Physics Forums | Science Articles, Homework Help, Discussion**