Sentence examples for multivariate normal density from inspiring English sources

Since the last integrand in (A.6) is a multivariate normal density which integrates to unity, then we get (A7).

The discriminant fits a multivariate normal density to each data group, with a pooled estimate of covariance defined by (12).

Since we are working in RGB color space, the multivariate normal density distribution of a color value is given by (20).

To accelerate their calculations, the topology is assumed to be known and the likelihood is approximated using a multivariate normal density.

We approximate the density of U with a multivariate normal density and denote the sample estimate of the six by six variance covariance matrix as.

For the final prediction, classify was called using the 'diaglinear' option, which fits a multivariate normal density to each group with a pooled estimate of covariance with the non-diagonal entries of the covariance matrix set to zero.

We show in File S1 that if the genotypes of some individuals are unobserved, the joint density of (g 1, g 2 ) is not multivariate normal; rather, it is a mixture of multivariate normal densities (see File S1).

Following the previous development in Section 3, we shall transform the multivariate normal densities as follows: Upon demonstrating that is independent of given we finish by going from The density is where: Letting we define: where =, is equal to the vector = and is the remaining × matrix.

The full density factors into independent multivariate normal densities (MVNs) for each row of Λ k * : π (λ j | y j, b j, e a j, F, ψ r j ) ∼ N (ψ r j − 1 C − 1 F T (y j − X b j − Z e a j ), C − 1 ), where C = ψ r j − 1 F T F + Diag (φ i j τ j ).

Similar reasoning was also used by de los Campos et al. [ 39] who clearly showed that conditional on M2, g1 has a mixture of scaled-multivariate normal densities.

While we agree that conditional on M2, g1 has a mixture of scaled-multivariate normal densities, it must be noted that even the unconditional distribution of g1 is only approximately normal.