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The marginal alignment probability can be calculated efficiently using the forward backward algorithm (Lafferty et al., 2001).
Equation (5) is similar to the definition of TM-score except that the latter does not have a term for the marginal alignment probability.
Since w i is equal to 0 at a gap position, Equation (5) sums the marginal alignment probabilities over all the alignment positions with the match state (i.e. state M).
We additionally expect it will be feasible to develop simple accelerated heuristics for identifying optimal or near-optimal switch points from joint to marginal alignment modes, in order to bypass the need for full dynamic programming.
The expected TM-score of one threading alignment is defined as follows: (5) where N(A) is the smaller length of the two proteins and MAG i is the marginal alignment probability at alignment position i.
Given two residues of a pair of proteins, the marginal alignment probability is equal to the accumulative probability of all possible alignments of this pair of proteins in which these two residues are aligned to each other.
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Left marginal mode alignments may only be extended by aligning left residues x i (central panel of Fig. 2), and right marginal mode alignments may only be extended by aligning right residues x j (center right panel of Fig. 2).
It became popular because of its analytic tractability (cf. Siddharthan et al., 2005), and it is simple enough so that the marginal likelihood of an alignment, given a phylogenetic tree can be computed analytically.
The model permits an analytical computation of the marginal likelihood of an alignment given a phylogenetic tree, thereby offering an evaluation of how the estimated model generalizes to novel observations.
However, these mismatches only constitute a marginal fraction within the final alignments obtained after filtering of the initial dataset.
Our approach considers all the possible alignments of reads to HLA allele sequences, and calculates the marginal likelihood of data from gapped alignments of reads to the reference sequences, in which deletions and insertions as well as SNP sites are naturally considered.
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