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. 2022 Sep 5;25(1):188–202. doi: 10.1093/biostatistics/kxac035

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© The Author 2022. Published by Oxford University Press.

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

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Fig. 3 — Computation times (seconds) for exact and approximate calculations as a function of increasing number of observations . Computational time (-axis) as a function of observations (-axis) to calculate the individual components of (a) exact including (i) the dissimilarity matrix (purple) scaling , (ii) the adjacency matrix (orange), and (iii) the most expensive operation (pink) scaling . Note, is only shown for = 100 and 500 observations, but the trend is shaded in for the other observations; (b,c) have different y-axes than (a). The diagonal line between (a) and (b) connects the 20-s ticks of these two axes. (b) Approximate estimation (HPE) using the grid search procedure including (i) the dissimilarity matrix (blue) scaling and (ii) the HPE algorithm to estimate (orange) scaling ; (c) approximate estimation using the bootstrap procedure (HPB) (purple), which scales similarly to HPE without the computational expense required for calculating . Note (b) and (c) have a different -axis scale than (a) for an zoomed in visualization of time.

Inline graphic — Computation times (seconds) for exact and approximate calculations as a function of increasing number of observations . Computational time (-axis) as a function of observations (-axis) to calculate the individual components of (a) exact including (i) the dissimilarity matrix (purple) scaling , (ii) the adjacency matrix (orange), and (iii) the most expensive operation (pink) scaling . Note, is only shown for = 100 and 500 observations, but the trend is shaded in for the other observations; (b,c) have different y-axes than (a). The diagonal line between (a) and (b) connects the 20-s ticks of these two axes. (b) Approximate estimation (HPE) using the grid search procedure including (i) the dissimilarity matrix (blue) scaling and (ii) the HPE algorithm to estimate (orange) scaling ; (c) approximate estimation using the bootstrap procedure (HPB) (purple), which scales similarly to HPE without the computational expense required for calculating . Note (b) and (c) have a different -axis scale than (a) for an zoomed in visualization of time.