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Binom is the binomial probability of observing S k out of N k given mean survival (e^{-widehat {y_{k}} t}).
The correlation score was measured using -log(P) for correlation and log(P) for anti-correlation, where P is the p-value corresponding to the binomial probability of observing the corresponding frequency shift [ 15].
For a gene to be considered up-regulated by σB, the binomial probability of observing as many reads in the Δ sigB strain as those observed for 10403S had to be < 0.05 for each of the four possible combinations.
The binomial probability of observing two or more de novo mutations at a specified position in a set of 41 cases (including one affected parent) was calculated and corrected for the target size of the human exome (24.75 Mb).
Conversely, for a gene to be considered down-regulated by σB, the binomial probability of observing as many reads as those observed for Δ sigB had to have q-values < 0.05 for each of the four possible combinations.
Binomial probability of observing x infected reads aligned to a base, out of n total reads aligning to that base, estimated based on the HMM described in the text, and median corrected induction (log2 scale) for each class (see Methods for details).
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We calculated the significance of this (potential) module preferring the type 1 combination as the binomial tail probability of observing at least m1 successful experiments in n experiments, each of which had a success rate of P k.
Finally, we calculated the binomial tail probability of observing n of the 7390 mRNAs containing target sites of all k miRNAs in this group as the statistical significance of this group of miRNAs.
Based on zero-inflated binomial models, the probability of observing perch larvae increased from approximately 20% in low AV habitats to nearly 100% in dense AV habitats (pseudo-R2 = 0.54).
The probability under the heterozygous model was calculated as the binomial probability of the observed counts assuming a probability of 0.5 for each allele.
Given a pool with s of n reads with the alternate allele, we used the binomial distribution to compute the probability of observing s or fewer successes in n trials with success probability.
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