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The posterior sum n g is naturally determined by the amount of adaptation data.
With the probability of Gaussian component g, we then compute the ML mean vector: {boldsymbol{mu}}_g^{mathrm{ML}}=frac{1}{n_g}_nright1}^Npleft(gBig|{mathbf{x}}_nright){mathbf{x}}_n (19 where ( {n}_g={varSigma}_{n=1}^Npleft gBig|{mathbf{x}}_nright) ) which is called posterior sum.
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We then multiply the probabilities calculated from base genotypes, allelic phase information, and allele frequencies, rescale (to ensure all posteriors sum to 1), and output the posterior probability for each HLA allele pair.
Score normalization based on term-dependent thresholding, rank normalization and mapping back to posteriors, sum-to-one normalization, and machine learning.
with Z k a normalizing value to ensure that the posterior probabilities sum up to 1.
where p z x | X i ) is the likelihood function, P(X i ) is the prior probability of class X i, and P (z x ) is the evidence, computed as P ( z x ) = ∑ i ∈ S p ( z x | X i ) P ( X i ), which is a scale factor that ensures that the posterior probabilities sum to one.
The special form of logistic regression model ensures that the posterior probabilities sum to 1, i.e. ∑ c Pr (Class = c| Z = z) = 1.
These methods, as well as orthology detection methods under non-default parameter settings, can be set in LatentGOLD software as "Inactive Covariates" (i.e. they do not play a role in LCA analysis), and their error rates are obtained by rescaling average posteriors to sum to 1 within classes.
For every potential interaction either ancestral or extant our algorithm computes the posterior probability, summed over an ensemble of parsimonious and near-parsimonious histories, which the interaction exists.
For the case of Bayesian phylogenies, we also used their specific posterior probabilities whose sum was scaled to 1.
There is also no reason to expect the modes of the marginal posterior distributions to sum-to-unity: something that is not an issue if the full posterior distribution is used in down-stream analyses.
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