jointprior: Calculates the joint prior distribution

In ClausDethlefsen/deal: Learning Bayesian Networks with Mixed Variables

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) 

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 prob method for network objects, which is called by the network function.
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, the procedure tries to set a value as low as possible.
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.

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]=jointalpha[i]

and

phi[i] = (nu[i] -1)Sigma[i]

if phiprior="bottcher", see Bottcher(2001) and

phi[i] = nu[i](rho[i] -2)Sigma[i]/(nu[i]+1)

if phiprior="heckerman", see Heckerman, Geiger and Chickering (1995).

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.

Author(s)

Susanne Gammelgaard Bottcher,
Claus Dethlefsen [e-mail].

References

Bottcher, S.G. (2001). Learning Bayesian Networks with Mixed Variables, Artificial 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, 20: 197-243.

Shachter, R.D. and Kenley, C.R. (1989), Gaussian influence diagrams. Management Science, 35:527-550.

See Also

network, prob

Examples

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

## Not run: savenet(rats.nw,file("rats.net"))
## Not run: rats.nw <- readnet(file("rats.net"))
## Not run: rats.nw <- prob(rats.nw,rats)
## Not run: rats.prior <- jointprior(rats.nw,12)

ClausDethlefsen/deal documentation built on Nov. 18, 2022, 11:38 p.m.