Conjugate prior for Gaussian mixture estimation

Requests maximum a posteriori (MAP) estimation of the Gaussian profile means and covariances under the conjugate prior of Fraley and Raftery (2007), exactly as mclust::priorControl() does for mclust::Mclust(). Pass the result as multilpa(prior = ). The prior keeps covariances away from singularity, which is what lets a many-profile or many-indicator model be fitted where maximum likelihood degenerates.

Usage

prior_control(shrinkage = 0.01, mean = NULL, dof = NULL, scale = NULL)

# S3 method for class 'latents_prior'
print(x, ...)

Arguments

shrinkage

Non-negative prior precision factor for the means, kappa; mclust's default 0.01. Zero leaves the means unshrunk.

mean

Optional prior mean, one value per continuous indicator, in the indicators' own units. Naming one needs a positive shrinkage.

dof

Optional prior degrees of freedom, a single number.

scale

Optional prior scale: a single positive number for an axis-parallel or spherical structure, or a positive-definite d by d matrix for an ellipsoidal one.

x

A latents_prior object.

...

Ignored.

Value

An object of class latents_prior: a list with shrinkage, mean, dof and scale, the last three NULL where the default is to be computed from the data.

print() returns x invisibly.

Details

Every argument left NULL takes mclust::defaultPrior()'s value, computed from the indicators being fitted: the prior mean is their column means, the degrees of freedom are d + 2 for d indicators, and the scale is (1/G)^(2/d) times the sample covariance (ellipsoidal structures) or times the average sample variance (axis-parallel and spherical structures), for G profiles.

Conditions

Raises latents_bad_argument for a negative or non-finite shrinkage, a mean with a zero shrinkage, or a non-positive dof or scale.

References

Fraley, C., & Raftery, A. E. (2007). Bayesian regularization for normal mixture estimation and model-based clustering. Journal of Classification, 24, 155–181. doi:10.1007/s00357-007-0004-5

See also

multilpa(), whose prior argument takes this.

Examples

prior_control()
#> Conjugate prior (Fraley & Raftery, 2007)
#>   shrinkage: 0.01
#>   mean:      mclust default (from the data)
#>   dof:       mclust default (from the data)
#>   scale:     mclust default (from the data)
prior_control(shrinkage = 0)
#> Conjugate prior (Fraley & Raftery, 2007)
#>   shrinkage: 0
#>   mean:      mclust default (from the data)
#>   dof:       mclust default (from the data)
#>   scale:     mclust default (from the data)