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Given two multi-variate gaussians distrubtions, given by mean & covariance, G1(m1,sigma1) & G2(m2,sigma2), what are the formulae to find the product i.e G1 * G2 ? And if one was looking to implement this in c++, what would an efficient way of doing it?

Go easy, I am primarily a computer scientist and not a pure mathematician.

Any help much appreciated.

  • 1
    What do you mean by "find the product"? Do you want to do the *distribution* of the product or something else? Also, what "product" are you interested in? Is $G_1 \cdot G_2$ an inner (i.e., dot) product? An outer product? Something else? Recall that $G_1$ and $G_2$ are *vectors*, so, in particular, the inner product wouldn't make sense if $G_1$ and $G_2$ are of differing dimensions.2012-06-11
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    I suspect what the question was intended to mean is this: What is the _distribution of_ the product of two random variables, whose distributions are those Gaussian distributions? Probably they were intended to be independent---that's an assumption people often forget to mention. Definitely the poster should clarify.2012-06-11
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    I mean the d-dimensional multivariate case of this http://www.tina-vision.net/docs/memos/2003-003.pdf2012-06-11
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    Essentially the maths being conducted in this matlab function (in the case where there are two d-dimensional gaussian distributions. http://www.ee.ic.ac.uk/hp/staff/dmb/voicebox/doc/voicebox/gausprod.html2012-06-12

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