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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.

G

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).

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.

Value

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

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.

See Also

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")
mclust

Gaussian Mixture Modelling for Model-Based Clustering, Classification, and Density Estimation

v5.4.10
GPL (>= 2)
Authors
Chris Fraley [aut], Adrian E. Raftery [aut] (<https://orcid.org/0000-0002-6589-301X>), Luca Scrucca [aut, cre] (<https://orcid.org/0000-0003-3826-0484>), Thomas Brendan Murphy [ctb] (<https://orcid.org/0000-0002-5668-7046>), Michael Fop [ctb] (<https://orcid.org/0000-0003-3936-2757>)
Initial release
2022-05-20

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