# What is Sigma?

###### Identification of microbes and accurate estimation of their relative abundance are crucial subjects in metagenomic analysis. Existing taxonomic classification methods are unsuitable for metagenomic biosurveillance due to the following three factors. First, reference genomes including complete genomes of pathogenic bacteria are required. Second, strain-level genome identification from the same species is essential. Third, statistical confidence evaluation of the metagenomic analysis is recommended. We developed Sigma (**S**train-level **I**nference of **G**enomes from **M**etagenomic **A**nalysis), a novel sequence similarity-based approach for strain-level identification of genomes from metagenomic analysis for biosurveillance. Nucleotide-level alignments analysis using maximum likelihood estimation empowers Sigma to estimate the relative abundances and likelihood ratios of each genome accurately given a list of reference genomes. Hybrid parallel architecture of the SIGMA allows its computation to be scalable from desktops to supercomputers for different sizes of metagenomic reads and reference datasets.

# Sigma Overview

# Sigma Algorithm

#### The foundation of all Sigma’s statistical inferences is a simple probabilistic model for sampling reads with mismatches from genomes at unknown abundances. The Sigma probabilistic model permits maximum likelihood estimation (MLE) of the relative abundances of all genomes in terms of the percentages of reads sampled from these genomes. Importantly, we proved the convexity of the objective function of the MLE such that Sigma can guarantee to attain a global optimum solution using interior point non-linear programming (NLP) provided in the Ipopt library.

## Strain-level Identification of Genomes from Metagenomic Analysis for Biosurveillance