multivariate gaussian mle

  1. C

    Differentiation Involving Determinant.

    I have to compute the following differentiation : \frac{\partial}{\partial\sigma^2}\det[\mathbf X_{p\times n}'(\sigma^2 \mathbf I_{n}+\mathbf Z_{n\times q}\mathbf G_{q\times q}\mathbf Z_{q\times n}')^{-1}\mathbf X_{n\times p}], where \sigma^2 is a scalar, \det denotes determinant, \mathbf...
  2. K

    Multivariate gaussian, MLE

    How do you take the derivative of \ln p(X|\mu,\Sigma)=-\frac{N D}{2}\ln(2\pi)-\frac{N}{2}\ln|\Sigma|-\frac{1}{2}\sum_{n=1}^N(x_n-\mu)^T\Sigma^{-1}(x_n-\mu) with respect to \Sigma?