| localmaster {deal} | R Documentation |
Joint distribution of a node and its parents from the joint prior.
localmaster(family,nw,prior=jointprior(nw))
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. |
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]]
Susanne Gammelgaard Bøttcher alma@math.auc.dk,
Claus Dethlefsen dethlef@math.auc.dk.
Further information about deal can be found at:
http://www.math.auc.dk/novo/deal.