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In the optimal filter, these two variances shall statistically match each other reasonably well.
The mean was then taken of these two variances of cross-covariances.
The net effect of these two variances is $5 extra cost at site 1.
The difference between these two variances gave an estimate of −0.05 for the gametic phase disequilibrium covariance.
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Thus, these two variance matrices cannot be estimated simultaneously.
However, it would be possible to model these two variance components separately, if multiple observations (measurements) were made on each individual, for multiple individuals per species.
These two variance-covariance matrices and the relationship matrix (A, based on the LPRI pedigree) were used with the rmvnorm [ 31] function of R Version 3.0.2 [ 29] to generate random effects drawn from multivariate normal distributions (equations (7) and (8)) for a simulated population.
These four variances are then employed to evaluate the gradient ∇g y) of the input pixel y, which is defined as ∇ g ( y ) = K ( H ) 2 + K ( V ) 2 + K ( L D ) 2 + K ( R D ) 2 (6).
The mean of these four variances was used as the overall residual variance of the herd cluster.
These four variances are estimated in the model using flat prior distributions, i.e., σ u 2, σ s 2, σ g 2, σ e 2 ∼ Bern.
For a line segment L ij, näively, these three variances take time proportional to the number of points explained by the line to compute, leading to a O(n) algorithm for computing the matrix ℋ. Below we will show that each of σrΔ s, σr t, and σr u can indeed be computed incrementally and in constant time from previous computations resulting in a O(n) algorithm.
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Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com