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It is shown that the resulting mixture converges weakly to the prior component.
The mean is preserved by choosing μ in (21b) to be the mean of the prior component.
S&M uses the maximum eigenvalue of the prior component as the split direction, and in this case, it gives the same results as choosing the direction randomly.
Convergence properties are more rarely discussed, but, for example, in [2] a GM splitting that converges weakly to the prior component is presented.
The affine transformation is chosen to be such that after transformation the split dimension is aligned with the direction of the maximum nonlinearity and such that the resulting mixture is a good approximation of the prior component.
We propose in this paper a way of splitting a prior component called Binomial Gaussian mixture (BinoGM) and show that when the number of components is increased, the pdf and cumulative distribution function (cdf) of the resulting mixture converge to the pdf and cdf of the prior component.
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Gaussian mixture filters (GMFs) work in such a manner that the prior components are split, if necessary, into smaller components to reduce the linearization error within a component.
The splitting direction is chosen to be the eigenvector of the prior covariance closest to this direction, and the prior components are split into two or three components that preserve the mean and covariance of the original component.
In splitting a prior component, the parameters are chosen such that the mean and covariance are preserved.
So far, we have discussed the update of a prior component with a measurement at a single time step.
Taxa-relatedness questions completed by individuals had lower rates of correct answers coupled with correct reasoning compared with the prior group component of the evolution unit exam (Table 4), excluding the individual component of the evolution unit exam due to poor question structure (see Discussion).
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