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.