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The hyperparameters (left{ {upsilon,lambda,gamma,kappa } right} ) are estimated by maximum likelihood in: begin{aligned} log ( {p {y / x})})=-frac{1}{2}y^Tleft[ {K( {X,X})+sigma ^2I} right] ^{-1}y-frac{1}{2}leftleft| {K( {X,X})+sigma ^2I} right| -frac{n}{2}log 2}log
Marker allele frequencies were estimated by maximum likelihood in multigenerational families with SOLAR.
For each sample, a map of the Hurst exponent was estimated for each participant by maximum likelihood in the wavelet domain [2] and registered into MNI standard space by affine transformation.
Branch lengths of the tree comprising all species analyzed were estimated by Maximum Likelihood in TREE-PUZZLE v5.2 [119], using the consensus topology inferred by NJ analysis with PAM-like distances.
We calculated neutral Fst estimates using nucleotide p-distance for intron 1, as well as modified Nei and Gojobori dS at exon 2. We then computed functional divergence at exon 2 using the amino acid experimental exchangeability distance (EX) [81] estimated by maximum likelihood in HYPHY, for the 65 sites with dN/dS≤1 and for the 19 sites with dN/dS>1 separately.
The practical range was estimated by maximum likelihood in R using the package "geoR" [ 39], based on an exponential model.
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Mixture model parameters were estimated by maximum likelihood via the expectation-maximization algorithm in the FlexMix package [ 17] in the R project.
Estimate the model under the null by maximum likelihood either in the time domain or in the frequency domain, making sure that it satisfies the identification conditions stated in Sect.
Taking into account the theoretical results obtained in the previous sections, the step by step testing procedure for dynamic misspecification of the unobserved components can be described as follows: 1. Estimate the model under the null by maximum likelihood either in the time domain or in the frequency domain, making sure that it satisfies the identification conditions stated in Sect.
In each iteration, the (complex) reference distribution is approximated using a simple probability distribution; we illustrate the method by using a multinomial distribution, whose parameters are estimated by maximum likelihood estimation in each iteration, using the conformations generated in the previous iteration.
Site-specific likelihoods were calculated by maximum likelihood optimization in Treefinder using the same model specifications as for phylogenetic inference [ 22].
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