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(D ) An example to highlight the second step in (A ) that the directionality between two transcript profiles was found by multiple testing of the standardized partial variances of the nodes.
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Our results show that compared to simple random sampling and random balance design sampling, sensitivity indices (ratios of partial variances to variance of a specific model output) estimated by search-curve based sampling generally have higher precision but larger underestimations.
The variance of the model outputs was decomposed into correlated and uncorrelated partial variances to provide insight into parameter dependency and interaction.
This is done by estimating a pairwise ordering of the nodes from the data using multiple testing of the log-ratios of standardized partial variances, and by subsequent projection of this partial ordering onto the GGM.
Until now, the FAST analysis is mainly confined to the estimation of partial variances contributed by the main effects of model parameters, but does not allow for those contributed by specific interactions among parameters.
I calculated the relative variance as the partial variance for a given term divided by the maximum partial variance value in the model.
The theoretical derivation of partial variances contributed by higher-order interactions and the calculation of their corresponding estimation errors in different sampling schemes can help us better understand the FAST method and provide a fundamental basis for FAST applications and further improvements.
Hypothesis tests are constructed to reduce the effect of sampling errors on the estimation of partial variances.
We also analytically calculate the potential errors and biases in the estimation of partial variances.
A second approximation implicit in our algorithm concerns the determination of the ordering of the nodes, which is done by multiple testing of pairwise ratios of standardized partial variances.
Subsequently, a partial ordering of the nodes is established by multiple testing of the log-ratio of standardized partial variances.
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Since I tried Ludwig back in 2017, I have been constantly using it in both editing and translation. Ever since, I suggest it to my translators at ProSciEditing.

Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com