@@ -48,7 +48,7 @@ This function is a structural Monte Carlo Markov Chain Model Choice (MC)^3 sampl

The classical (MC)^3 is unbiased but inefficient in mixing, the two radical MCMC alternative move are known to massively accelerate mixing without introducing biases. But those move are computationally expensive. Then low frequencies are advised. The REV move is not necessarily ergotic , then it should not be used alone.

The parameter \code{start.dag} can be: "random", "hc" or user defined. If user select "random" then a random valid DAG is selected. The routine used favourise low density structure. If "hc" (for Hill-climber: \link[abn:heuristic_search]{searchHeuristic} then a DAG is selected using 100 different searches with 500 optimization steps. A user defined DAG can be provided. It should be a named square matrix containing only zeros and ones. The DAG should be valid (i.e. acyclic).

The parameter \code{start.dag} can be: "random", "hc" or user defined. If user select "random" then a random valid DAG is selected. The routine used favourise low density structure. If "hc" (for Hill-climber: \link[abn:search_heuristic]{searchHeuristic} then a DAG is selected using 100 different searches with 500 optimization steps. A user defined DAG can be provided. It should be a named square matrix containing only zeros and ones. The DAG should be valid (i.e. acyclic).

The parameter \code{prior.choice} determines the prior used within each individual node for a given choice of parent combination. In Koivisto and Sood (2004) p.554 a form of prior is used which assumes that the prior probability for parent combinations comprising of the same number of parents are all equal. Specifically, that the prior probability for parent set G with cardinality |G| is proportional to 1/[n-1 choose |G|] where there are n total nodes. Note that this favours parent combinations with either very low or very high cardinality which may not be appropriate. This prior is used when \code{prior.choice=2}. When prior.choice=1 an uninformative prior is used where parent combinations of all cardinalities are equally likely. When \code{prior.choice=3} a user defined prior is used, defined by \code{prior.dag}. It is given by an adjacency matrix (squared and same size as number of nodes) where entries ranging from zero to one give the user prior belief. An hyper parameter defining the global user belief in the prior is given by \code{prior.lambda}.

@@ -323,4 +323,4 @@ to structure discovery in Bayesian networks. Machine Learning, 50:95–125, 2003

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* Goudie, R. J., and Mukherjee, S. (2016). A Gibbs Sampler for Learning DAGs. Journal of machine learning research: JMLR, 17(30), 1-39.

* Kuipers, J. and Moffa, G. (2017). Partition MCMC for Inference on Acyclic Digraphs, Journal of the American Statistical Association, 112:517, 282-299, DOI: 10.1080/01621459.2015.1133426

* Scutari, M. (2010). Learning Bayesian Networks with the bnlearn R Package. Journal of Statistical Software, 35(3), 1 - 22. doi:http://dx.doi.org/10.18637/jss.v035.i03.

* Scutari, M. (2010). Learning Bayesian Networks with the bnlearn R Package. Journal of Statistical Software, 35(3), 1 - 22. \doi{http://dx.doi.org/10.18637/jss.v035.i03.}