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Availability and implementation: A Python script implementing the empirical algorithm is freely available at http://sgjlab.org/empirical-go/.
The paper discusses challenges in implementing the Empirical Bayes design when less than ideal data are available.
Data was normalised by variance stabilizing normalization (VSN; [78]) and differentially expressed genes were detected using the 'Limma' (Linear Models for Microarray Analysis) package [79]; implementing the empirical Bayes linear modelling approach [80].
Arrays were normalized using quantile normalization, and expression estimates were calculated using GC-RMA, implementing the empirical Bayes estimate for non-specific binding [ 34].
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In this study, the Good-Turing estimator (SGT) [ 30] is used to implement the empirical Bayes.
ERα: estrogen receptor α; TF: transcription factor; E2: 17-estradiol; MCF7: luminal-like breast cancer cells; OHT: 4-OH tamoxifen; ERE: estrogen response elements; TFBS: TF binding site; EM: Expectation-Maximization; CS designed part of the computational study, implemented the empirical Beyes model and drafted part of the manuscript.
However, under certain circumstances the branch-specific test of selection can lack power and so we also used the branch-site test of selection [26], [30] implementing the Bayes empirical Bayes (BEB [26]) method to identify sites under selection.
Accordingly, we implemented the following empirical test of phase robustness based on simulated errors and thresholds; these were chosen conservatively to avoid over-assigning profiles patterns as cyclic.
Because the LRT suggested the presence of positively selected sites, we implemented the Bayes empirical Bayes (BEB) method [ 14] to calculate posterior probabilities for each site in this gene.
For kernel density estimation, the empirical probability distribution implementing the Variable Kernel Method with Gaussian Smoothing of the Apache Commons Math 3.6 API [15] is used.
The total absorption μa is implemented in the empirical path length model, while the modeled effective path length τ is adjusted simultaneously as a function of the total absorption, according to Eq. (3).
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