sp {hmm.discnp} | R Documentation |
Returns the probabilities that the underlying hidden state is equal to each of the possible state values, at each time point, given the observation sequence. Also can return the fitted conditional means, if requested, given that the observations are numeric.
sp(y, object = NULL, tpm, Rho, ispd=NULL, means = FALSE)
y |
The observations on the basis of which the probabilities
of the underlying hidden states are to be calculated. May be
a sequence of observations, or a list each component of which
constitutes a (replicate) sequence of observations. If y is
missing it is set equal to the y component of object ,
given that that object and that component exist. Otherwise an
error is given.
|
object |
An object of class hmm.discnp as returned by
hmm() .
|
tpm |
The transition probability matrix for the underlying hidden
Markov chain. Ignored if object is not NULL .
Ignored if object is not NULL (in which
case tpm is extracted from object ).
|
Rho |
The matrix of probabilities specifying the distribution of
the observations, given the underlying state. The rows of this
matrix correspond to the possible values of the observations, the
columns to the states. Ignored if object is not NULL
(in which case Rho is extracted from object ).
|
ispd |
Vector specifying the initial state probability distribution
of the underlying hidden Markov chain.
Ignored if object is not NULL (in which
case ispd is extracted from object ).
If both object and ispd are NULL then
ispd is calculated to be the stationary distribution
of the chain as determined by tpm .
|
means |
A logical scalar; if means is TRUE then the
conditional expected value of the observations (given the
observation sequence) is calculated at each time point.
If means is TRUE and the observation values
are not numeric, then an error is given.
|
Then conditional mean value at time t is calculated as
SUM_k gamma_t(k)*mu_k
where gamma_t(k) is the conditional probability (given the observations) that the hidden Markov chain is in state k at time t, and mu_k is the expected value of an observation given that the chain is in state k.
If means
is TRUE
then the returned value is
a list with components
probs |
The conditional probabilities of the states at each time point. |
means |
The conditional expectations of the observations at each time point. |
Otherwise the returned value consists of probs
as
described above.
If there is a single vector of observations y
then
probs
is a matrix whose rows correspond to the states
of the hidden Markov chain, and whose columns correspond to
the observation times. If the observations consist of a
list of observation vectors, then probs
is a list
of such matrices, one for each vector of observations.
Likewise for the means
component of the list returned
when the argument means
is TRUE
.
Rolf Turner
r.turner@auckland.ac.nz
http://www.math.unb.ca/~rolf
hmm()
, mps()
,
viterbi()
, pr()
,
fitted.hmm.discnp()
P <- matrix(c(0.7,0.3,0.1,0.9),2,2,byrow=TRUE) 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) y.num <- sim.hmm(rep(300,20),P,R) fit.num <- hmm(y.num,K=2,verb=TRUE) cpe1 <- sp(object=fit.num,means=TRUE) # Using the estimated parameters. cpe2 <- sp(y.num,tpm=P,Rho=R,means=TRUE) # Using the ``true'' parameters.