localmaster               package:deal               R Documentation

_L_o_c_a_l _m_a_s_t_e_r

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

     Joint distribution of a node and its parents from the joint prior.

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

     localmaster(family,nw,prior=jointprior(nw))

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

      nw: an object of class `network'.

  family: vector of integers, giving indices of node and parents of the
          node.

   prior: a list describing parameter priors, generated by
          `jointprior'.

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

     The procedure is intended for internal use and is called by
     `cond.node'. 

     For the discrete part of the network, the master is the marginal
     distribution of the discrete nodes in the family.

     For the mixed part of the network, for each configuration i of the
     discrete variables in `family', the joint parameter priors are
     given by `jointprior' as

              p(m[i]|Sigma[i]) = N(mu[i],Sigma[i]/nu[i])


                   p(Sigma[i]) = IW(rho[i],Phi[i])

     where `IW' denotes the inverse Wishart distribution.

     Then, the local master for configuration i is deduced for the
     family A as

 Sigma[A intersect Gamma|i[A intersect Delta]] ~ IW(rho[i[A intersect Delta]],tildePhi[A intersect Gamma|i[A intersect Delta]])


 m[A intersect Gamma|i[A intersect Delta]]|Sigma[A intersect Gamma|i[A intersect Delta]] sim N(bar.mu[A intersect Gamma|i[A intersect Delta]], Sigma[A intersect Gamma|i[A intersect Delta]]/nu[A intersect Delta])

     where Gamma is the set of continuous nodes and Delta is the set of
     discrete nodes. Furthermore,

 rho[i[A intersect Delta]] = sum_{j:j[A intersect Delta]=i[A intersect Delta]} rho[j]

     and likewise for nu[i[A intersect Delta]] and Phi[i[A intersect
     Delta]]. Finally,

 barmu[A intersect Delta] ( sum_{j:j[A intersect Delta]=i[A intersect Delta]} mu[j] nu[j] )/nu[i[A intersect Delta]]

_A_u_t_h_o_r(_s):

     Susanne Gammelgaard Bttcher alma@math.auc.dk, 
     Claus Dethlefsen dethlef@math.auc.dk.

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

     Further information about deal can be found at:
     <URL: http://www.math.auc.dk/novo/deal>.

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

     `cond.node'

