.BG
.FN estepEEE
.TL
E-step for constant-variance MVN mixture models
.SH DESCRIPTION
E-step for estimating conditional probabilities from parameter estimates in an
MVN mixture model having constant variance and possibly one Poisson noise term.
.CS
estepEEE(data, mu, sigma, prob, eps, Vinv)
.PP
.RA
.AG data
matrix of observations.
.RC mu
matrix whose columns are the Gaussian group means.
.RC sigma
group variance matrix.
.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
Lower bound on the reciprocal condition estimate for the cholesky factor of
the covariance matrix. Default : `sqrt(.Machine$double.eps)'.
.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 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
`estep', `meEEE', `mstepEEE'
.EX
> data <- matrix(aperm(iris, c(1,3,2)), 150, 4)
> cl <- mhclass(mhtree(data, modelid = 4),3)
> z <- meEEE( data, ctoz(cl))
> Mstep <- mstepEEE(data, z)
> estepEEE( data, Mstep$mu, Mstep$sigma, Mstep$prob)

.KW clustering
.WR

