.BG
.FN bic
.TL
BIC for parameterized MVN mixture models
.SH DESCRIPTION
Bayesian Information Criterion for MVN mixture models with possibly one 
Poisson noise term.
.CS
bic(data, modelid, z, eps, tol, itmax, equal = F, noise = F, Vinv)
.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 ...
other arguments, including a quantity `eps' for determining singularity
in the covariance, and the following:
.OA
.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. If `z' is missing,
a single cluster is assumed (all noise if `noise = T').
.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 equal
Logical variable indicating whether or not the mixing proportions are
equal in the model. The default is to assume they are unequal.
.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 the function `hypvol'
.RT
An object of class `"bic"' which is the Bayesian Information Criterion for the
given mixture model and given conditional probabilites. The model parameters 
and reciprocal condition estimate are returned as attributes.
.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
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).

R. Kass and A. E. Raftery, Bayes Factors. \fIJournal of the American 
Statistical Association\fR90:773-795 (1995).
.SA
`me', `mstep'
.EX
> data <- matrix(aperm(iris, c(1,3,2)), 150, 4)
> cl <- mclass(mclust(data, modelid = 4),3)
> z <- me( data, ctoz(cl), modelid = 3)
> bic(data, modelid = 3, z = z)

.KW clustering
.WR

