R: Default conjugate prior for Gaussian mixtures

defaultPrior {mclust} | R Documentation

## 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

`mclustBIC`, `me`, `mstep`, `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")

[Package mclust version 5.4.5 Index]