.BG
.FN mstepVI
.TL
M-step for spherical, varying volume MVN mixture models
.SH DESCRIPTION
M-step for estimating parameters given conditional probabilities in an MVN 
mixture model having varying spherical variances and possibly one Poisson noise
term.
.CS
mstepVI(data, z, eps, equal = F, noise = F, Vinv)
.PP
.RA
.AG data
matrix of observations.
.AG z
matrix of conditional probabilities. `z' should have a row for each observation
in `data', and a column for each component of the mixture.
.OA
.AG eps
Lower bound on the estimated values of sigma-squared. 
Default : `.Machine$double.eps'
.AG equal
Logical variable indicating whether or not to assume equal proportions in the
mixture. Default : `F'.
.AG noise
Logical variable indicating whether or not to include a Poisson noise term in
the model. Default : `F'.
.AG Vinv
An estimate of the inverse hypervolume of the data region (needed only if
`noise = T'). Default : determined by function `hypvol'
.RT
A list whose components are the parameter estimates corresponding to `z':
.RC mu
matrix whose columns are the Gaussian group means.
.RC sigma
group variance matrix.
.RC prob
probabilities (mixing proportions) for each group (present only when
`equal = T').
.br
The loglikelihood and reciprocal condition estimate are returned as attributes.
.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
`mstep', `meVI', `estepVI'
.EX
> data <- matrix(aperm(iris, c(1,3,2)), 150, 4)
> cl <- mhclass(mhtree(data, modelid = 2),3)
> z <- meVI( data, ctoz(cl))
> mstepVI(data, z)


.KW clustering
.WR

