We conducted analysis of the differential abundance of OTUs in different samples by fitting a local regression model with a negative binomial distribution to the data and testing for differential abundance with a likelihood ratio test as implemented in the R package DESeq2 (Love et al. 2014) and in conjunction with the Phyloseq package (McMurdie and Holmes 2013).
We computed the gene expression indexes for each gene across the 11 human tissues (a total of 33 samples), by fitting the probe level data to the Li-Wong model [6], implemented in the affy package of Bioconductor (http://www.bioconductor.org/).
We estimated the subtype status of clinical samples by fitting a Bayesian probit regression model with the subtype-specific enrichment scores for cell lines.
To assess differentially expressed miRNAs, we first estimated the fold changes and standard errors between two groups of samples by fitting a linear model for each miRNA with the 'lmFit' function of LIMMA package (Smyth et al, 2005).
To assess differentially-expressed miRNA, we first estimated the fold changes and standard errors between two groups of samples by fitting a linear model for each probe with the lmFit function of LIMMA package in R. Then we applied an empirical Bayes smoothing to the standard errors from the linear model previously computed with eBayes function.
We estimated the relationship between n-1 and the logistic regression coefficients for the given sample size by fitting the following equation based on the additive definition of the bias As the sample size increases, n → ∞, the bias converges to zero (lim n →∞ b1 n-1 = 0), thus the intercept corresponds to unbiased estimate of the population parameter value.
The Monte Carlo program SIMNRA was used to evaluate the sample compositions by fitting the peaks corresponding to the individual elements in the measured spectra.
This approach enabled robust lateral PSF width estimation under the sparse sampling conditions by fitting each lateral PSF to a 2D Gaussian surface whose FWHM was then calculated.
The alignment of the fibrils with respect to the stem axis was determined from the distribution of azimuthal intensity of cellulose diffraction peaks of the stem sliver samples, described by fitting to one or more Gaussian functions [ 29, 30].
The chemical speciation of each sample was determined by fitting a linear combination of model compounds to each XANES spectrum (Additional file 1: Figure SI.3).
