The estimations were done using maximum likelihood methods, which is considered one of the most appropriate approaches for small samples with autocorrelated errors [21],[21].
In [11], this is done using maximum likelihood criterion, whereas a least square based method looking for the minimum of Euclidean distance between received signal samples and a local replica of their noiseless components is presented in [12].
Model estimation was done using Maximum Likelihood (rather than Restricted Maximum Likelihood) to permit comparisons among models using Akaike's Information Criterion AICC).
Phylogenetic inferences were done using maximum parsimony (MP) and maximum likelihood (ML).
Usually a pairwise analysis of genomes in a set is carried out with a metric being computed that reflects the similarity between the genomes, this can be done using a maximum parsimony score, a threshold parsimony score (e.g. [ 14]) or deriving a phylogenetic distance.
Confirmatory studies of responsive airways, potentially assessed first by diurnal peak flow, can be done using post-bronchodilator maximum expiratory flow volume curves and methacholine challenges.
Once, the parametric model(s) for the severity distribution has been selected, the estimation of unknown parameters can be done using the method of moments (MM), Maximum Likelihood (ML, used in the empirical part) or Ordinary Least Square (OLS).
When the number of genes is fairly small, say, n<5000 computation of the left maximum eigenvector can be done using a built-in function in various software packages.
The selected representative sequences are indicated in the phylogeny in red in Additional file 2. The final multiple alignment including 113 sequences is shown in Additional file 5. Phylogenetic reconstruction was done using the maximum likelihood method (implemented in PHYML version 2.4.4) and the maximum parsimony method (implemented in PHYLIP version 3.65).
Supervised classification was done using the maximum likelihood algorithm for 3 spectral bands corresponding to green, red and near infrared.
