Sentence examples for by a scale matrix from inspiring English sources
The multivariate generalization of the Gamma is a Wishart, characterized by a scale matrix.
Corresponding to the penalties that 'borrow strength' from the phenotypic covariance matrix considered above, a penalty which regularizes the estimate of Σ G by shrinking it towards Σ p can be obtained by using Σ p as a scale matrix.
Dawid [15] and Giudici [16] show that, under the previous assumptions, the posterior distribution of the variance-covariance matrix (Sigma) is a hyper Wishart distribution with (alpha +n) degrees of freedom and a scale matrix given by: begin{aligned} T_{n}=T_{0}+S_{n} end{aligned} (10 where (S_{n}) is the sample variance-covariance matrix.
Finally, W is a scaling matrix used to balance the contributions of the observables (usually by scaling each temporal series with respect to its maximum value).
This is expected since the nonlinearities are known with a scaling matrix Ω (we have seen that the scaling matrix is canceled by W0 since W0 = HΩ-1).
In this case, the inverse covariance matrix of the channel estimation error can be approximated by a scaled identity matrix C η − 1 = X 0 H C n − 1 X 0 ≈ γ · ℐ (34).
Hence, ( mathbf {W}^{H}_{01} mathbf {W}_{01}) can be better approximated by a scaled identity matrix the larger P is, where begin{array}{*{20}l} mathbf{W}^{H}_{01} mathbf{W}_{01} approx mathbf{I}_{{M} {Q}} frac{{P}}{ {Q}}.
We then develop LMS-type algorithms by replacing the covariance matrix with a scaled identity matrix under the constraint that the determinant of the covariance matrix is preserved.
This method starts with an initially diagonal S scale matrix, and uses the inverse of this matrix to eliminate the deformation caused by scaling.
Within our penalized (RE ML framework, this can be achieved by substituting the structured matrix for the scale matrix Ω in (Eq. 10).
We now adapt the preconditioner for settings with hanging knots by replacing the scaling matrix D (i ) in (42) by a modified diagonal matrix D A (i ).
