7 bnlearn network
The default and recommended Bayesian network in BayesNetty is given by the bnlearn algorithm. All future extensions are intended to be built upon this approach. For a given data set and network structure the likelihood can be calculated under specific distributional assumptions, namely that discrete nodes follow a multinomial distribution and continuous nodes a normal distribution, with distributional parameters determined by the values of the incoming parent nodes. The manner in which the likelihood is calculated can vary between Bayesian network algorithms. See Scutari and Denis (2014) and Nagarajan et al. (2013) for further details of bnlearn methodology and R package.
The network score for a bnlearn network may be set to either the log likelihood, AIC or BIC using the -input-network-score option, see section 6.1.
NOTE: The BIC network score is based on the definition used by bnlearn (see Scutari and Denis (2014)) such that BIC = log(L) - (d/2)log(n), where L is the likelihood of the network for the given data set, d is the number of parameters and n is the number of individuals. This is the original definition used by Swartz in 1978, see Schwarz (1978), rather than subsequent definitions of BIC which are multplied by negative two (for example see Wit et al. (2012)). Therefore in BayesNetty the BIC will always be negative and higher values of the network score imply a better fit network. (Whichever definition of BIC that one considers, the closer the BIC is to zero the better the model fit.)
The AIC network score in BayesNetty is defined similarly to the BIC such that AIC = log(L) - d, where L and d are defined as above. Therefore higher values of the negatively valued AIC (closer to zero) imply a better network fit to the given data set.
Naturally if only the log likelihood is used then higher values imply a better network fit.
