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First, a value is sampled from the posterior conditional distribution (or full conditional) of the latent underlying variables, then from the posterior conditional distribution of the factor loadings and so forth.
Moreover, under the trilinear condition, the Wiener measure twisted by the diffusion matrix becomes stationary for the limit and we show that the solution of the limit equation exists globally in time when the initial value is sampled from the stationary measure.
Recent studies have revealed that many commercial network interface cards are adopted with a non-uniform distribution for generating backoff values during contention periods in order to obtain a better performance [2, 3].The p-persistent-based model in [4] shows that the backoff value is sampled by using the p value in a geometric distribution.
To obtain a valid velocity, a random value is sampled in [1 − M, M − 1] while v ~ p k t + 1 exceeds its domain.
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For TP lineups, one value was sampled from a normal distribution with a mean of d′ = 1.5 and a standard deviation of 1, and five values were sampled from a distribution with a mean of 0 and standard deviation of 1; for TA lineups, six values were randomly sampled from an N 0,1) distribution.
The actual value was sampled conditional on the data as part of the Gibbs sampler.
For each simulation, a random value was sampled from these distributions, and the outcomes of the model were calculated.
For a single permutation, a strain phenotype value was sampled from each of the 13 distributions, and the set of 13 values was permuted.
In both groups, ewes with a low estimated overall breeding value were sampled, since these are not relevant for producing replacements.
For each given GC-content target distribution, a set of individual target GC values is sampled from the distribution and antaRNA is run for each.
Longitude values are sampled along the strike of the rupture.
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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