|
Number of founders |
N |
Number of offspring |
T |
Number of markers (loci) |
|
Hidden founder haplotype at locus t
|
|
Hidden founder haplotype matrix
|
|
Hidden ancestral origins at locus t in offspring i
|
|
on maternally (m) or paternally (p) derived chromosome |
|
Genotype at locus t in offspring i that is completely determined by and
|
|
Hidden true genotype at locus t in offspring i
|
|
Observed genotype at locus t in offspring i
|
|
Observed offspring genotype matrix
|
|
Observed genotypes for all founders at locus t
|
|
Observed founder genotype matrix
|
|
Genotypes containing uncertain allele U
|
|
Number of reads for alleles 1 or 2 |
|
Allelic error probability for offspring, independent of read depths |
|
Allelic error probability for founders, independent of read depths |
|
Phred quality score |
ε |
Sequencing error probability
|
|
Prior probability of at locus 1 in offspring i
|
|
Prior transition probability from to
|
|
likelihood at locus t in offspring i
|
|
Posterior probability of conditional on and genotypic data from loci 1 to t
|
|
Unnormalized conditional posterior probability of
|
|
Posterior probability of conditional on genotypic data from loci 1 to t
|
|
Hats denote maximum likelihood estimates |
|
Single genotype call if probability of most probable genotype is greater than threshold
|
|
Impute if probability of most probable genotype is greater than threshold
|
|
Correct if probability of most probable genotype is greater than threshold
|