text: user349: I have a huge amount of ~20x human WGS samples, aligned, and all SNVs that were called with GATK under standard germline parameters set.
  What I need to do is to model SNVs Allele Frequency (AF) for different underlying Copy Numbers. I'd better provide a toy example. For particular genomic region X:
  If X is presented by 2 copies for the particular samples, we expect AF to be super-close to 1 or to 0.5.
  If X is presented by 4 copies, I expect any particular AF to be close to 0.25, 0.5, 0.75 or 1.
  Of course, I can use Binomial Distribution for these purposes. However, as we know, the distribution is not exactly Binomial due to alignment/sequencing biases and the median AF for all heterozygous SNVs is more close to 0.48 but not to 0.5 as we would expect. Another thing: for high copy numbers we expect higher coverages. And GATK use several filters so I suppose that we will not see SNVs with AF like 0.125 (in case if the segment has ploidy 8) - despite the super high coverage there GATK may reject this "weird" AF.
  I have read several papers that model SNVs AFs (and I agree that Beta Binomial Distribution may be quite accurate), however, I was not convinced enough that I should use the particular modelling. From your experience (in case if you do SNVs calling), which probabilistic distribution should I use? How should I estimate parameters for each of them (should I expect for CN4 AF=0.5 more frequent than AF=0.75 or vice versa, how to estimate this from data)?
  UPD: For simplicity we can say that we have a lot of previously identified regions with ploidy different from CN2, and I can take these coordinates from here. So I can use more or less "supervised" learning for parameters' estimation.
  
  user492: I don't have enough experience to answer which probabilistic distribution should be used.
  However, this questions also also asks how to estimate parameters of the distributions. If a binomial distribution is chosen, then Heng Li's paper titled "A statistical framework for SNP calling, mutation discovery, association mapping and population genetical parameter estimation from sequencing data" 1 is probably the definitive one. Section 2.3.1 of that paper describes an EM algorithm for estimating allele frequencies from multiple samples under the assumption of Hardy-Weinberg equilibrium for arbitrary but constant ploidy.
  
original_text: 349: <p>I have a huge amount of ~20x human WGS samples, aligned, and all SNVs that were called with GATK under standard germline parameters set.</p>
  
  <p>What I need to do is to model SNVs Allele Frequency (AF) for different underlying Copy Numbers. I'd better provide a toy example. For particular genomic region X:</p>
  
  <p><em>If X is presented by <strong>2</strong> copies for the particular samples, we expect AF to be super-close to 1 or to 0.5.</em></p>
  
  <p><em>If X is presented by <strong>4</strong> copies, I expect any particular AF to be close to 0.25, 0.5, 0.75 or 1.</em></p>
  
  <p>Of course, I can use <em>Binomial Distribution</em> for these purposes. However, as we know, the distribution is not exactly Binomial due to alignment/sequencing biases and the median AF for all heterozygous SNVs is more close to 0.48 but not to 0.5 as we would expect. Another thing: for high copy numbers we expect higher coverages. And GATK use several filters so I suppose that we will not see SNVs with AF like 0.125 (in case if the segment has ploidy 8) - despite the super high coverage there GATK may reject this "weird" AF.</p>
  
  <p>I have read several papers that model SNVs AFs (and I agree that Beta Binomial Distribution may be quite accurate), however, I was not convinced enough that I should use the particular modelling. From your experience (in case if you do SNVs calling), which probabilistic distribution should I use? How should I estimate parameters for each of them (should I expect for CN4 AF=0.5 more frequent than AF=0.75 or vice versa, how to estimate this from data)?</p>
  
  <p><strong>UPD:</strong> For simplicity we can say that we have a lot of previously identified regions with ploidy different from CN2, and I can take these coordinates from <a href="http://www.nature.com/ng/journal/v47/n3/full/ng.3200.html" rel="noreferrer">here</a>. So I can use more or less "supervised" learning for parameters' estimation.</p>
   492: <p>I don't have enough experience to answer which probabilistic distribution should be used.</p>
  
  <p>However, this questions also also asks how to estimate parameters of the distributions. If a binomial distribution is chosen, then Heng Li's paper titled "A statistical framework for SNP calling, mutation discovery, association mapping and population genetical parameter estimation from sequencing data" <a href="https://doi.org/10.1093/bioinformatics/btr509" rel="nofollow noreferrer">1</a> is probably the definitive one. Section 2.3.1 of that paper describes an EM algorithm for estimating allele frequencies from multiple samples under the assumption of Hardy-Weinberg equilibrium for arbitrary but constant ploidy.</p>
  