| forward {tileHMM} | R Documentation |
These functions calculate the forward and backward variables for a given model and observation sequence. All computations are carried out in log-space.
## S4 method for signature 'hmm': forward(hmm, obs) ## S4 method for signature 'hmm': backward(hmm, obs)
hmm |
An object of class hmm or one of its subclasses representing the hidden Markov model. |
obs |
A vector containing the observation sequence. |
backward returns the N times T matrix of (log transformed) backward variables,
where N is the number of states of hmm and T is the length of obs.
forward returns a list with components
logProb |
log[P(obs|hmm)] |
alpha.scaled |
The matrix of log transformed forward variables. This has the same dimensions
as the matrix returned by backward |
Peter Humburg
Rabiner, L. R. 1989 A tutorial on hidden Markov models and selected applications in speech recognition. Proceedings of the IEEE, 77(2), 257–286.
## create two state HMM with t distributions
state.names <- c("one","two")
transition <- c(0.1, 0.02)
location <- c(1, 2)
scale <- c(1, 1)
df <- c(4, 6)
model <- getHMM(list(a=transition, mu=location, sigma=scale, nu=df),
state.names)
## obtain observation sequence from model
obs <- sampleSeq(model, 100)
## calculate the probability of the observation given the model
fwd <- forward(model, obs)
fwd$logProb
## compute posterior probabilities
bwd <- backward(model,obs)
post <- bwd + fwd$alpha.scaled
post <- t(t(post) - apply(post,2,logSum))
## get sequence of most likely states
state.seq <- state.names[apply(post,2,which.max)]