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Then, we estimate the coarse CFO by seeking the maximum of the equivalent likelihood function according to the reconstructed EMV.
If we settle on the point of probabilistic independence PE(H) = P(H) as a natural common zero, and so subtract 1 from each multiplicative measure,[13] then equivalent likelihood terms appear in both columns.
Unlike coarse CFO-estimation that only EMV requires to recover, the fine CFO-estimation usually need the recovered signal r at Nyquist rate to construct the equivalent likelihood function (see Subsection 4.1).
From (3), the equivalent likelihood function (Lambda left ({Delta widetilde f} right)) can be rewritten as Lambda left({Delta widetilde f} right) buildrel Delta over = {left| {Psi left({Delta widetilde f} right)} right|^{2}} = {left| {{{mathbf{r}}^{T}} cdot {boldsymbol{Gamma }}left {Delta widetilde f} right)} right|^{2}}.
In case the search finds multiple gene trees with statistically equivalent likelihood and the same minimum reconciliation cost, it outputs the one that has the highest likelihood.
The incorporation of SNPs creates new sets of conditional independence relations, allowing us to distinguish between gene regulatory networks with equivalent likelihood.
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Then, an interpolation method is employed to construct the equivalent likelihood-function.
It is important to note that given the complexity of the model, our search of parameter space gives us not one but a family of parameter sets with equivalent likelihoods.
In fact, six dimensions must be fitted in the reduced rank form (FARR6) to produce equivalent likelihoods to the best FA model with three dimensions.
At the DRA, both M2a and M8 had equivalent likelihoods and suggested that approximately 10% of sites were possibly under positive selection (ω = 3.40) with the remaining sites under purifying selection (ω = 0.04) (Table 5).
In some common situations in which the alternative model information matrix is singular under the null, we derive one-sided extremum tests, which are asymptotically equivalent to likelihood ratio tests, and explain how to compute reliable Wald tests.
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