mps: Most probable states.

In hmm.discnp: Hidden Markov Models with Discrete Non-Parametric Observation Distributions

Most probable states.

Description

Calculates the most probable hidden state underlying each observation.

Usage

mps(y, model = NULL, tpm, Rho, ispd=NULL, warn=TRUE)

Arguments

y	The observations for which the underlying most probable hidden states are required. May be a sequence of observations in the form of a vector or a one or two column matrix, or a list each component of which constitutes a (replicate) sequence of observations. It may also be an object of class "multipleHmmDataSets" as returned by rhmm() with nsim>1. If y is missing, it is extracted from model (whence it will not be of class "multipleHmmDataSets"!) provided that model and its y component are not NULL. Otherwise an error is given.
model	An object describing a fitted hidden Markov model, as returned by hmm(). In order to make any kind of sense, model should bear some reasonable relationship to y.
tpm	The transition probability matrix for a hidden Markov model; ignored if model is non-null. Should bear some reasonable relationship to y.
Rho	An object specifying the probability distributions of the observations (“emission” probabilities) for a hidden Markov model. See hmm(). Ignored if model is non-null. Should bear some reasonable relationship to y.
ispd	A vector specifying the initial state probability distribution for a hidden Markov model, or a matrix each of whose columns are trivial (“delta function”) vectors specifying the “most probable” initial state for each observation sequence. This argument is ignored if model is non-null. It should bear some reasonable relationship to y. If both ispd and model are NULL then ispd is taken to be the stationary distribution of the chain, calculated from tpm.
warn	Logical scalar; in the bivariate setting, should a warning be issued if the two matrices constituting Rho (bivariate independent case) or the array constituting Rho (bivariate dependent case) have not got relevant dimension names? (Note that if this is so, then the corresponding dimension names are formed from the sorted unique values of the appropriate columns of y. And if this is so, then the user should be sure that the ordering of the entries of Rho corresponds properly to the the sorted unique values of y.) This argument is passed to the utility function check.yval() which actually issues the warning if warn=TRUE.

Details

For each t the maximum value of gamma_t(i), i.e. of the (estimated) probability that the state at time t is equal to i, is calculated, and the value of the state with the corresponding index is returned.

Value

If y is a single observation sequence, then the value is a vector of corresponding most probable states.

If y is a list of replicate sequences, then the value is a list, the j-th entry of which constitutes the vector of most probable states underlying the j-th replicate sequence.

If y is of class "multipleHmmDataSets" then the value returned is a list of lists of the sort described above.

Warning

The sequence of most probable states as calculated by this function will not in general be the most probable sequence of states. It may not even be a possible sequence of states. This function looks at the state probabilities separately for each time t, and not at the states in their sequential context.

To obtain the most probable sequence of states use viterbi().

Author(s)

Rolf Turner [e-mail]

References

Rabiner, L. R., "A tutorial on hidden Markov models and selected applications in speech recognition," Proc. IEEE vol. 77, pp. 257 – 286, 1989.

See Also

hmm(), rhmm(), viterbi()

Examples

## Not run: 
P <- matrix(c(0.7,0.3,0.1,0.9),2,2,byrow=TRUE)
rownames(P) <- 1:2
R <- matrix(c(0.5,0,0.1,0.1,0.3,
              0.1,0.1,0,0.3,0.5),5,2)
set.seed(42)
lll   <- sample(250:350,20,TRUE)
set.seed(909)
y.num <- rhmm(ylengths=lll,nsim=1,tpm=P,Rho=R,drop=TRUE)
fit.num <- hmm(y.num,K=2,verb=TRUE)
s.1 <- mps(y.num,fit.num)
s.2 <- mps(y.num,tpm=P,ispd=c(0.25,0.75),Rho=R)
# The order of the states has got swapped; 
# note that ifelse(s.1[[1]]=="1","2","1") is much
# more similar to s.2[[1]] than is s.1[[1]].

## End(Not run)

hmm.discnp documentation built on Sept. 26, 2022, 5:05 p.m.