defaultPrior             package:mclust             R Documentation

_D_e_f_a_u_l_t _c_o_n_j_u_g_a_t_e _p_r_i_o_r _f_o_r _G_a_u_s_s_i_a_n _m_i_x_t_u_r_e_s.

_D_e_s_c_r_i_p_t_i_o_n:

     Default conjugate prior specification for Gaussian mixtures.

_U_s_a_g_e:

     defaultPrior(data, G, modelName, ...) 

_A_r_g_u_m_e_n_t_s:

    data: The name of the function specifying the conjgate prior. The
          default function is 'defaultPrior', which can be used a
          template for   

       G: The number of mixture components. 

modelName: A character string indicating the model: 
           "E": equal variance  (one-dimensional) 
           "V": variable variance (one-dimensional)
            "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  

     ...: One or more of the following:

        _d_o_f The degrees of freedom for the prior on the variance.  The
             default is 'd + 2', where 'd' is the dimension of the
             data.

        _s_c_a_l_e The scale parameter for the prior on the variance.  The
             default is 'var(data)/G^(2/d)', where 'd' is the domension
             of the data.

        _s_h_r_i_n_k_a_g_e 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.

        _m_e_a_n The mean parameter for the prior.  The default value is
             'colMeans(data)'. 

_D_e_t_a_i_l_s:

     'defaultPrior' is as a default prior specification   for EM within
     _MCLUST_. It is usually not necessary to invoke 'defaultPrior'
     explicitly (it does not appear in the examples below because it is
     the default function name in 'priorControl'). This function allows
     considerable flexibility in the prior specification, and can be
     used as a template for further users that want to specify their
     own conjugate prior beyond what the arguments will allow.

_V_a_l_u_e:

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

_R_e_f_e_r_e_n_c_e_s:

     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). Bayesian regularization for
     normal mixture estimation and model-based clustering. Technical
     Report, Department of Statistics, University of Washington.

     C. Fraley and A. E. Raftery (2006). MCLUST Version 3 for R: Normal
     Mixture Modeling and Model-Based Clustering,  Technical Report no.
     504, Department of Statistics, University of Washington.

_S_e_e _A_l_s_o:

     'mclustBIC', 'me', 'mstep', 'priorControl'

_E_x_a_m_p_l_e_s:

     # 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])

