.BG
.FN estep
.TL
E-step for parameterized MVN mixture models
.SH DESCRIPTION
E-step for estimating conditional probabilities from parameter estimates in an
MVN mixture model having possibly one Poisson noise term.
.CS
estep(data, modelid, mu, ...)
.PP
.RA
.AG data
matrix of observations.
.AG modelid
An integer specifying a parameterization of the MVN covariance matrix defined 
by volume, shape and orientation charactertistics of the underlying clusters. 
The allowed values for `modelid' and their interpretation are as follows:
`"EI"' : uniform spherical, `"VI"' : spherical, `"EEE"' : uniform variance,
`"VVV"' : unconstrained variance, `"EEV"' : uniform shape and volume,
`"VEV"' : uniform shape.
.AG mu
matrix whose columns are the Gaussian group means.
.AG ...
additional arguments, as follows:
.AG sigmasq
.AG sigma
group variances (`sigmasq' - spherical models) or covariances (`sigma' -
elliposidal models)
.OA
.AG prob
mixing proportions (probabilities) for each group. If `prob' is missing, 
the number of groups is assumed to be the number of columns in `mu' (no
noise). A Poisson noise term will appear in the conditional probabilities if
`length(prob)' is equal to `ncol(mu)+1'.
.AG eps
Tolerance for determining singularity in the covariance matrix. The precise
definition of `eps' varies the parameterization, each of which has a default.
.AG Vinv
An estimate of the inverse hypervolume of the data region (needed only if
`prob' indicates a noise term). Default : determined by function `hypvol'
.RT
the conditional probablilities corresponding to the parameter estimates.
The loglikelihood is returned as an attribute.
.SH NOTE
The reciprocal condition estimate returned as an attribute ranges in value
between 0 and 1. The closer this estimate is to zero, the more likely it is
that the corresponding EM result (and BIC) are contaminated by roundoff error.
.SH REFERENCES
G. Celeux and G. Govaert, Gaussian parsimonious clustering models,
\fIPattern Recognition, \fR28:781-793 (1995).

A. P. Dempster, N. M. Laird and D. B. Rubin, Maximum Likelihood from
Incomplete Data via the EM Algorithm, \fIJournal of the Royal Statistical
Society, Series B, \fR39:1-22 (1977).

C. Fraley and A. E. Raftery, How many clusters? Which clustering method?
Answers via model-based cluster analysis. \fIComputer Journal,
\fR41:578-588 (1998).

C. Fraley and A. E. Raftery, \fIMCLUST:Software for model-based cluster
and discriminant analysis. \fRTechnical Report No. 342, Department of
Statistics, University of Washington (1998).

G. J. MacLachlan and T. Krishnan, The EM Algorithm and Extensions, Wiley
(1997).
.SA
`me', `mstep'
.EX
> data <- matrix(aperm(iris, c(1,3,2)), 150, 4)
> cl <- mhclass(mhtree(data, modelid = "VI"),3)
> z <- me( data, ctoz(cl), modelid = "VVV")
> Mstep <- mstep(data, modelid = "VVV", z)
> estep( data, modelid = "VVV", Mstep$mu, Mstep$sigsq, Mstep$prob)

.KW clustering
.WR

