defaultPrior: Default conjugate prior for Gaussian mixtures

Description

Default conjugate prior specification for Gaussian mixtures.

Usage

defaultPrior(data, G, modelName, …)

Arguments

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.

The number of mixture components.

modelName

A character string indicating the model: "E": equal variance (univariate) "V": variable variance (univariate) "EII": spherical, equal volume "VII": spherical, unequal volume "EEI": diagonal, equal volume and shape "VEI": diagonal, varying volume, equal shape "EVI": diagonal, equal volume, varying shape "VVI": diagonal, varying volume and shape "EEE": ellipsoidal, equal volume, shape, and orientation "EEV": ellipsoidal, equal volume and equal shape "VEV": ellipsoidal, equal shape "VVV": ellipsoidal, varying volume, shape, and orientation. A description of the models above is provided in the help of 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 MCLUST up to version 4.4.

…

One or more of the following:

dof: The degrees of freedom for the prior on the variance. The default is d + 2, where d is the dimension of the data.
scale: The scale parameter for the prior on the variance. The default is var(data)/G^(2/d), where d is the dimension of the data.
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.
mean: The mean parameter for the prior. The default value is colMeans(data).

Value

A list giving the prior degrees of freedom, scale, shrinkage, and mean.

Details

defaultPrior is a function whose default is to output the default prior specification for EM within MCLUST. Furthermore, 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. 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. Journal of Classification 24:155-181.

Examples

Run this code

# NOT RUN {
# 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")
# }

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