E-Step of EM Algorithm for DTHMM
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*m transition probability matrix of the hidden Markov chain. |
distn |
is a character string with the distribution name, e.g. |
pm |
is a list object containing the current (Markov dependent) parameter estimates associated with the distribution of the observed process (see |
pn |
is a list object containing the observation dependent parameter values associated with the distribution of the observed process (see |
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
hat{u}_{ij} = E[u_{ij} | X^{(n)}] = Pr{ C_i=j | X^{(n)} = x^{(n)} } ,
and v[i,j,k]
is
hat{v}_{ijk} = E[v_{ijk} | X^{(n)}] = Pr{ C_{i-1}=j, C_i=k | X^{(n)} = x^{(n)} } ,
where j,k = 1, ..., m and i = 1, ..., n.
A list
object is returned with the following components.
u |
an n*m matrix containing estimates of the conditional expectations. See “Details”. |
v |
an n*m*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).
Cited references are listed on the HiddenMarkov manual page.
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