1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
|
\name{defaultPrior}
\alias{defaultPrior}
\title{
Default conjugate prior for Gaussian mixtures
}
\description{
Default conjugate prior specification for Gaussian mixtures.
}
\usage{
defaultPrior(data, G, modelName, \dots)
}
\arguments{
\item{data}{
A numeric vector, matrix, or data frame of observations. Categorical
variables are not allowed. If a matrix or data frame, rows
correspond to observations and columns correspond to variables.
}
\item{G}{
The number of mixture components.
}
\item{modelName}{
A character string indicating the model: \cr\cr
\code{"E"}: equal variance (univariate) \cr
\code{"V"}: variable variance (univariate)\cr
\code{"EII"}: spherical, equal volume \cr
\code{"VII"}: spherical, unequal volume \cr
\code{"EEI"}: diagonal, equal volume and shape\cr
\code{"VEI"}: diagonal, varying volume, equal shape\cr
\code{"EVI"}: diagonal, equal volume, varying shape \cr
\code{"VVI"}: diagonal, varying volume and shape \cr
\code{"EEE"}: ellipsoidal, equal volume, shape, and orientation \cr
\code{"EEV"}: ellipsoidal, equal volume and equal shape\cr
\code{"VEV"}: ellipsoidal, equal shape \cr
\code{"VVV"}: ellipsoidal, varying volume, shape, and orientation. \cr\cr
A description of the models above is provided in the help of
\code{\link{mclustModelNames}}. Note that in the multivariate case
only 10 out of 14 models may be used in conjunction with a prior, i.e.
those available in \emph{MCLUST} up to version 4.4.
}
\item{\dots}{
One or more of the following:
\describe{
\item{\code{dof}}{
The degrees of freedom for the prior on the variance.
The default is \code{d + 2}, where \code{d} is
the dimension of the data.
}
\item{\code{scale}}{
The scale parameter for the prior on the variance.
The default is \code{var(data)/G^(2/d)},
where \code{d} is the dimension of the data.
}
\item{\code{shrinkage}}{
The shrinkage parameter for the prior on the mean.
The default value is 0.01.
If 0 or NA, no prior is assumed for the mean.
}
\item{\code{mean}}{
The mean parameter for the prior.
The default value is \code{colMeans(data)}.
}
}
}
}
\value{
A list giving the prior degrees of freedom, scale, shrinkage, and mean.
}
\details{
\code{defaultPrior} is a function whose default is to output the
default prior specification for EM within \emph{MCLUST}.\cr
Furthermore, \code{defaultPrior} can be used as a template to specify
alternative parameters for a conjugate prior.
}
\references{
C. Fraley and A. E. Raftery (2002).
Model-based clustering, discriminant analysis, and density estimation.
\emph{Journal of the American Statistical Association} 97:611-631.
C. Fraley and A. E. Raftery (2005, revised 2009).
Bayesian regularization for normal mixture estimation and model-based
clustering.
Technical Report, Department of Statistics, University of Washington.
C. Fraley and A. E. Raftery (2007).
Bayesian regularization for normal mixture estimation and model-based
clustering. \emph{Journal of Classification} 24:155-181.
}
\seealso{
\code{\link{mclustBIC}},
\code{\link{me}},
\code{\link{mstep}},
\code{\link{priorControl}}
}
\examples{
# default prior
irisBIC <- mclustBIC(iris[,-5], prior = priorControl())
summary(irisBIC, iris[,-5])
# equivalent to previous example
irisBIC <- mclustBIC(iris[,-5],
prior = priorControl(functionName = "defaultPrior"))
summary(irisBIC, iris[,-5])
# no prior on the mean; default prior on variance
irisBIC <- mclustBIC(iris[,-5], prior = priorControl(shrinkage = 0))
summary(irisBIC, iris[,-5])
# equivalent to previous example
irisBIC <- mclustBIC(iris[,-5], prior =
priorControl(functionName="defaultPrior", shrinkage=0))
summary(irisBIC, iris[,-5])
defaultPrior( iris[-5], G = 3, modelName = "VVV")
}
\keyword{cluster}
|
