Profile hidden Markov model: forward likelihood and Viterbi alignment

Each profile position has a match state with its own emission distribution, an insert state emitting from a background distribution, and a silent delete state. The forward recursion sums over alignments and Viterbi takes the maximum; the delete states are silent, so their recursion consumes no residue.

Usage

Hmmprf(seq, profile)

Arguments

seq

Residue indices, 0-based.

profile

Named list with match (L x A emissions), insert (background emissions) and trans (named list with mm, mi, md, im, ii, dm, dd).

Value

List with estimate, forward_logprob, viterbi_logprob, log_odds, background_logprob, n, method.

Details

Formula: seven transitions mm, mi, md, im, ii, dm, dd; forward sums and Viterbi maximises over the three state types.

References

Eddy (1998), Profile hidden Markov models, Bioinformatics 14(9):755-763, doi:10.1093/bioinformatics/14.9.755 ; Krogh, Brown, Mian, Sjolander and Haussler (1994), Journal of Molecular Biology 235(5):1501-1531. doi:10.1006/jmbi.1994.1104

Examples

# a 2-position DNA profile (A, C, G, T = 0..3) that prefers "AC"
tr <- list(mm = 0.9, mi = 0.05, md = 0.05, im = 0.9, ii = 0.1, dm = 0.9, dd = 0.1)
profile <- list(match = rbind(c(0.85, 0.05, 0.05, 0.05), c(0.05, 0.85, 0.05, 0.05)),
                insert = rep(0.25, 4), trans = tr)
Hmmprf(c(0, 1), profile)$log_odds         # high for the consensus
#> [1] 2.236926
Hmmprf(c(3, 2), profile)$log_odds
#> [1] -3.402198