5.12 thetaRatio

Estimate the ratio in heterozygosity (theta) between genomic regions

thetaRatio uses an MCMC (Metropolis-Hastings Algorithm) to estimate the ratio of the expected heterozygosity from sites in two different regions.

\[\Phi = log(\frac{\theta_1}{\theta_2})\]

5.12.1 Input

Required inputs :

--bam Input_bam_file.bam	Input bam file
--region1 region_1 --region2 region_2	Two files, region_1 and region_2 that define the regions of the two thetas.

Optional inputs :

--pmd "library_type:model_for_5'_read:model_for_3'_read" or --RGInfo

Library type followed by the model to be used for the 5-prime read-end and the 3-prime read-end which can be either “Exponential” or “Empiric”. All three arguments must be provided as a string, divided by colons (:). e.g. : –pmdModels “doubleStrand:Exponential:Exponential”. Used to specify Post-mortem damage parameters. Can also be provided as a .txt file (see PMDfor generating such a file). Default = Will assume there is no PMD in the data.

--recal recal_model or --RGInfo

A common recal model for all read groups.Used to specify Quality score recalibration parameters. Can also be provided as a .txt file (see recal for further information). Default = ‘-’, no recalibration is performed.

Specific Parameters :

• See Filter parameters to apply specific filters for bases, reads and parsing window setting.

Engine parameters that are common to all tasks can be found here.

5.12.2 Output

*_RGInfo.json	File containing read group info.
*_filterSummary.txt	File containing filter summary of general filter counts.
*_thetaRatioMCMC.txt.gz	File containing MCMC chain.

5.12.3 Usage Example

#! /bin/bash

# Set atlas path
atlas=$(dirname "$0")/../build/atlas

# Simulate a BAM File with specific theta
$atlas simulate --chrLength "10000,20000" --theta "0.001,0.002" --logFile simulate.out 

# Create region files
echo "chr1 1 10000" > region1.bed
echo "chr2 1 10000" > region2.bed

# 
$atlas thetaRatio --bam ATLAS_simulations.bam --region1 region1.bed --region2 region2.bed --logFile theta.out

5.12.4 Additional Information

Method

The likelihood function is:

\[ {P}(\boldsymbol{d}_1,\boldsymbol{d}_2|\theta_1,\theta_2, \boldsymbol{\pi}_1, \boldsymbol{\pi}_2) = \dfrac{\prod\limits_{i=1}^I \sum\limits_g \prod\limits_{j=1}^{n_i} \mathbb{P}(d_{1_{ij}}|g_i=g)\mathbb{P}(g_i=g|\theta_1,\boldsymbol{\pi}_1)}{\prod\limits_{i=1}^I \sum\limits_{g} \prod\limits_{j=1}^{n_i} \mathbb{P}(d_{2_{ij}}|g_i=g)\mathbb{P}(g_i=g|\theta_2,\boldsymbol{\pi}_2)} \] An MCMC is used to infer the posterior distribution for all parameters. Updates are performed for all: \((\boldsymbol{\pi})\) and \((\log(\theta_1))\) and \((\log(\theta_2))\).

\(U[0,1]\) prior is used for \((\log(\theta_1))\) and \((\log(\theta_1))\) and \(N(0, 1)\). is used for \((\boldsymbol{\pi})\).