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. 2021 May 13;71(1):121–138. doi: 10.1093/sysbio/syab037

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© The Author(s) 2021. Published by Oxford University Press on behalf of the Society of Systematic Biologists.

This is an Open Access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by-nc/4.0/) which permits unrestricted reuse, distribution, and reproduction in any medium, provided the original work is properly cited.

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Figure 2. — Uncertainty ellipses for SMP and GMRF. We show the improvement in asymptotic precision rendered by use of a smoothing prior for a segment skyline inference problem. The prior informed ellipse (red) is smaller in volume and has skewed principal axes relative to the purely data informed one (blue). All ellipses represent confidence with the indicating coordinate directions about their means, which are the log population sizes, . The covariance that smoothing introduces controls the skew of these ellipses. Here, , (total coalescent event count) and (this controls the prior influence see Equation 12). Larger values lead to over-reliance on the smoothing prior.

Inline graphic — Uncertainty ellipses for SMP and GMRF. We show the improvement in asymptotic precision rendered by use of a smoothing prior for a segment skyline inference problem. The prior informed ellipse (red) is smaller in volume and has skewed principal axes relative to the purely data informed one (blue). All ellipses represent confidence with the indicating coordinate directions about their means, which are the log population sizes, . The covariance that smoothing introduces controls the skew of these ellipses. Here, , (total coalescent event count) and (this controls the prior influence see Equation 12). Larger values lead to over-reliance on the smoothing prior.