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The estimated effect of EDU is much reduced when the true (generating) theta or the PVs are employed, as both can fully control for this effect.
Table 1 displays the results for this example and provides evidence of how estimates based on PVs and the true (generating) ability are quite similar, while estimates based on using EAP, MLE, or WLE are biased.
From these likelihoods, the ML/empirical Bayes posterior probability of each topology was calculated using a point prior that places prior density 1.0 on the ML branch lengths for that topology, with priors for the two topologies matching the true generating conditions.
The BI posterior probability of each topology was calculated by integrating over all eight branch length sets for that topology, using a prior distribution in which the probability of each topology and each branch length set on that topology matched the true generating conditions.
And more importantly, when the true generating model is included in the set of models being tested, the model selection tests choose the true generating model.
10.7554/eLife.04250.004 Figure 3. Model inferences when the true generating model differs from our distance-block-model prior.
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The true observation generating mechanism is generally assumed to be a member of the predictor stochastic source set (mathbb {M}) [20, 28].
The subset pivotality assumption is needed to ensure that control under a data generating distribution satisfying the complete null gives the desired control under the true data generating distribution, which may harbor any number of true nulls [ 43].
A simultaneous clustering parameter is defined as a function θ=Φ(P) of the true data generating distribution P, and an estimate is obtained by applying this function to the empirical distribution Pn.
Maximization of (4), using optimisation algorithms such as the Newton-Raphson, yields consistent estimates of θ, given correct specification of the model; that is, the true data generating process (DGP) is NB2-Logit.
This fragment is the more likely of the two possible contiguous sequences to be the true fragment generating the reads.
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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