deal (version 1.2-4)

jointprior: Calculates the joint prior distribution

Description

Given a network with a prob property for each node, derives the joint probability distribution. Then the quantities needed in the local master procedure for finding the local parameter priors are deduced.

Usage

jointprior(nw,N=NA,phiprior="bottcher",timetrace=FALSE) 
jointdisc(nw,timetrace=FALSE)
jointcont(nw,timetrace=FALSE)

Arguments

nw

an object of class network. Each node must have a prob property to describe the local probability distribution. The prob property is created using

N

an integer, which gives the size of the imaginary data base. If this is too small, NA's may be created in the output, resulting in errors in learn. If no N is given,

phiprior

a string, which specifies how the prior for phi is calculated. Either phiprior="bottcher" or phiprior="heckerman" can be used.

timetrace

a logical. If TRUE, prints some timing information on the screen.

Value

• A list with the following elements,
• jointalpha
  a table used in the local master procedure for discrete variables.
• jointnu
  a table used in the local master procedure for continuous variables.
• jointrho
  a table used in the local master procedure for continuous variables.
• jointmu
  a numeric matrix used in the local master procedure for continuous variables.
• jointsigma
  a list of numeric matrices (not used in further calculations).
• jointphi
  a list of numeric matrices used in the local master procedure for continuous variables.

Details

For the discrete part of the network, the joint probability distribution is calculated by multiplying together the local probability distributions. Then, jointalpha is determined by multiplying each entry in the joint probability distribution by the size of the imaginary data base N. For the mixed part of the network, for each configuration of the discrete variables, the joint Gaussian distribution of the continuous variables is constructed and represented by jointmu (one row for each configuration of the discrete parents) and jointsigma (a list of matrices -- one for each configuration of the discrete parents). The configurations of the discrete parents are ordered according to findex. The algorithm for constructing the joint distribution of the continuous variables is described in Shachter and Kenley (1989). Then, jointalpha, jointnu, jointrho, mu and jointphi are deduced. These quantities are later used for deriving local parameter priors. For each configuration i of the discrete variables, $$\nu_i=\rho_i=\alpha_i$$ and $$\phi_i = (\nu_i -1)\Sigma_i$$ if phiprior="bottcher", see B�ttcher(2001) and $$\phi_i = \nu_i(\rho_i -2)\Sigma_i/(\nu_i+1)$$ if phiprior="heckerman", see Heckerman, Geiger and Chickering (1995). The procedures jointcont and jointdisc are intended for internal use only.

References

B�ttcher, S.G. (2001). Learning Bayesian Networks with Mixed Variables, {\emArtificial Intelligence and Statistics 2001}, Morgan Kaufmann, San Francisco, CA, USA, 149-156. Heckerman, D., Geiger, D. and Chickering, D. (1995). Learning Bayesian networks: The combination of knowledge and statistical data. Machine Learning {\bf20}: 197-243. Shachter, R.D. and Kenley, C.R. (1989), Gaussian influence diagrams. Management Science {\bf35}:527-550. Further information about deal can be found at: http://www.math.auc.dk/novo/deal.

See Also

network, prob.network

Examples

data(rats)
rats.nw    <- network(rats)
rats.prior <- jointprior(rats.nw,12)

savenet(rats.nw,"rats.net")
rats.nw <- readnet("rats.net")
rats.nw <- prob.network(rats.nw,rats)
rats.prior <- jointprior(rats.nw,12)