Estep: E-Step of EM Algorithm for DTHMM
In HiddenMarkov: Hidden Markov Models

Description Usage Arguments Details Value Author(s) References See Also

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.

1	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 mm* 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

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 nm* matrix containing estimates of the conditional expectations. See “Details”.
`v`	an nmm array containing estimates of the conditional expectations. See “Details”.
`LL`	the current value of the log-likelihood.