dic                  package:BRugs                  R Documentation

_D_I_C

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

     These functions are used to evaluate the Deviance Information
     Criterion.

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

     dicSet()
     dicStats()
     dicClear()

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

     These functions are used to evaluate the Deviance Information
     Criterion (DIC; Spiegelhalter et al., 2002)  and related
     statistics - these can be used to assess model complexity and
     compare different models.  Most of the examples packaged with
     OpenBUGS contain an example of their usage.

     It is important to note that DIC assumes the posterior mean to be
     a good estimate of the stochastic parameters.  If this is not so,
     say because of extreme skewness or even bimodality,  then DIC may
     not be appropriate.  There are also circumstances, such as with
     mixture models,  in which OpenBUGS will not permit the calculation
     of DIC and so the menu option is greyed out.  Please see
     'help.WinBUGS' for restrictions.

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

     'dicStats' returns a data frame with columns: 

    Dbar: The posterior mean of the deviance, which is exactly the same
          as if the node  'deviance' had been monitored. This deviance
          is defined as -2 * log(likelihood):  'likelihood' is defined
          as p(y | theta), where y comprises all stochastic nodes given
          values (i.e. data),  and theta comprises the stochastic
          parents of y - 'stochastic parents' are the stochastic nodes 
          upon which the distribution of y depends, when collapsing
          over all logical relationships.

    Dhat: A point estimate of the deviance (-2 * log(likelihood))
          obtained by substituting in the  posterior means theta.bar of
          theta: thus Dhat = -2 * log(p(y | theta.bar)).

      pD: The effective number of parameters is given by pD = Dbar -
          Dhat.  Thus pD is the posterior mean of the deviance minus
          the deviance of the posterior means.

     DIC: The Deviance Information Criterion is given by DIC = Dbar +
          pD = Dhat + 2 * pD.  The model with the smallest DIC is
          estimated to be the model that would best predict a replicate
           dataset of the same structure as that currently observed.

_N_o_t_e:

     Users should ensure their simulation has converged before using
     these functions. If the MCMC simulation has an adaptive phase it
     will not be possible to make inference  using values sampled
     before the end of this phase.

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

     Spiegelhalter, D.J., Best, N.G., Carlin B.P., and van der Linde,
     A. (2002): Bayesian measures of model complexity and fit (with
     discussion). _J. Roy. Statist. Soc. B._ 64, 583-640.

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

     'BRugs', 'help.WinBUGS'

