Estep {HiddenMarkov} | R Documentation |
Performs the expectation step of the EM algorithm for a dthmm
process. This function is called by the BaumWelch
function. The Baum-Welch algorithm referred to in the HMM literature is a version of the EM algorithm.
Estep(x, Pi, delta, distn, pm, pn = NULL)
x |
is a vector of length n containing the observed process. |
Pi |
is the current estimate of the m times m transition probability matrix of the hidden Markov chain. |
distn |
is a character string with the distribution name, e.g. "norm" or "pois" . If the distribution is specified as "wxyz" then a probability (or density) function called "dwxyz" should be available, in the standard R format (e.g. dnorm or dpois ). |
pm |
is a list object containing the current (Markov dependent) parameter estimates associated with the distribution of the observed process (see dthmm ). |
pn |
is a list object containing the observation dependent parameter values associated with the distribution of the observed process (see dthmm ). |
delta |
is the current estimate of the marginal probability distribution of the m hidden states. |
Let u_{ij} be one if C_i=j and zero otherwise. Further, let v_{ijk} be one if C_{i-1}=j and C_i=k, and zero otherwise. Let X^{(n)} contain the complete observed process. Then, given the current model parameter estimates, the returned value u[i,j]
is
widehat{u}_{ij} = mbox{E}[u_{ij} , | , X^{(n)}] = Pr{C_i=j , | , X^{(n)} = x^{(n)} } ,,
and v[i,j,k]
is
widehat{v}_{ijk} = mbox{E}[v_{ijk} , | , X^{(n)}] = Pr{C_{i-1}=j, C_i=k , | , X^{(n)} = x^{(n)} },,
where j,k = 1, cdots, m and i = 1, cdots, n.
A list
object is returned with the following components.
u |
an n times m matrix containing estimates of the conditional expectations. See “Details”. |
v |
an n times m times m array containing estimates of the conditional expectations. See “Details”. |
LL |
the current value of the log-likelihood. |
The algorithm has been taken from Zucchini (2005).