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An EM algorithm for estimating can be found in Lander and Botstein (1989), and can be obtained by using the ordinary least-square method.
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Information on the statistical precision of the effect estimates can be found in the Technical Appendix.
Ages of major nodes are indicated by yellow circles, and the corresponding age estimates can be found in [Additional file 13 ].
In many thermodynamic models, including those examined in this study, the mathematical formula used to calculate the expression level is a rational function in which parameters to be estimated can be found in both the numerator and denominator [ 1, 2].
Full details on how this was estimated can be found in Additional file 1, and the results in Additional file 2: Tables S1 and Additional file 3: Table S2.
If, however, very accurate estimates are desired, a refined estimate can be found as described next.
In other words, each local estimate can be found independently of the other estimates.
Proof The proof of these standard estimates can be found, for instance, in [15].
This Markov type estimate can be found in various papers (see e.g. [11] for corresponding references).
We also mention the recent reference [12], where similar estimates can be found for nonlocal equations with unbounded kernels.
18 Stratification is also done by gender but no large diverging results were found, the estimates can be found in Table 9 in the Appendix.
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