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For each sample, we would like to calculate the likelihood of a set of reads assuming that we sequenced the correct sample, assuming we sequenced a sample related to the correct sample, or assuming we sequenced an incorrect sample. We would then like to flag samples where it appears likely that the wrong sample has been sequenced.  
 
For each sample, we would like to calculate the likelihood of a set of reads assuming that we sequenced the correct sample, assuming we sequenced a sample related to the correct sample, or assuming we sequenced an incorrect sample. We would then like to flag samples where it appears likely that the wrong sample has been sequenced.  
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If we have a list of bases that overlap a known genotype, we can calculate the probability of a match or mismatch at each base as:  
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If we have a list of bases that overlap a known genotype, we can will
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describe the probability of a matching of mismatching base using the
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following notation:
    
{| width="100%" cellspacing="1" cellpadding="1" border="1" summary="Summary of Variables Used Below"
 
{| width="100%" cellspacing="1" cellpadding="1" border="1" summary="Summary of Variables Used Below"
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| Definition
 
| Definition
 
|-
 
|-
| A/A  
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| <span class="texhtml">''A/A''</span>
 
| Previously known genotype; we only consider homozygous sites.
 
| Previously known genotype; we only consider homozygous sites.
 
|-
 
|-
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| Estimate error rate for the current base in the sequence data.
 
| Estimate error rate for the current base in the sequence data.
 
|}
 
|}
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Then, the probabilities of interest are:
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<math>
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P(match) = P_{ibd} (1 - \epsilon) + (1 - P_{ibd}) \epsilon
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P(no match) = P_{ibd} \epsilon + (1 - P_{ibd}) \epsilon
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</math>
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