Bayesian parameter estimation: multivariate Gaussians

(1 hours to learn)


Using the Bayesian framework, we can infer the posterior over the mean vector of a multivariate Gaussian, the covariance matrix, or both. Since multivariate Gaussians are widely used in probabilistic modeling, the computations that go into this are common motifs in Bayesian machine learning more generally.


This concept has the prerequisites:


  • Derive the conjugate priors for the multivariate distribution in three cases:
    • unknown mean, but known covariance
    • known mean, but unknown covariance
    • unknown mean and unknown covariance
  • Derive the posterior distributions for each of these cases.

Core resources (read/watch one of the following)


Supplemental resources (the following are optional, but you may find them useful)


See also