Is it possible to infer the parameters of a gaussian random variable by sampling from a distribution that is linearly dependent on the variable of interest? For example:

y = Ax + n


x ~ N(u,S)

n ~ N(0,Q)

A : known constant matrix

Q : known constant matrix

Can we infer the mean (u) and covariance matrix (S) of x from observations (samples) from the y distribution?

  • $\begingroup$ Are $A$ or $Q$ known? $\endgroup$ – Bridgeburners Jul 10 '17 at 14:47
  • $\begingroup$ Yes. Sorry. I have edited the post to indicate that $\endgroup$ – ejlouw Jul 11 '17 at 6:21

Given the distributions of $x$ and $n$, we know that $y \sim N(Au, A'SA+Q)$. Given that $A$ and $Q$ are known, and assuming you know the sample mean and variance of $y$, then it's a system of 2 equations with 2 unknowns, which you can easily solve.


Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.