@@ -44,7 +44,7 @@ The workhorse of the R package is the `mcmcabn()` function. It generates MCMC sa

**What is the structure of this document?**

We first illustrate the package with a simple example. Then some more theoretical details are provided. For a full description of the technical details we refer to the original publication [XXX].

We first illustrate the package with a simple example. Then some more theoretical details are provided. For a full description of the technical details we refer to the original publication.

# Simple *mcmcabn* example

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@@ -60,7 +60,7 @@ Once installed, the `mcmcabn` R package can be loaded using:

library(mcmcabn)

```

Let us start with a ranking example from the `bnlearn` R package [XXX]. The first example is about a small synthetic dataset from Lauritzen and Spiegelhalter (1988) about lung diseases (tuberculosis, lung cancer or bronchitis) and visits to Asia.

Let us start with a ranking example from the `bnlearn` R package from Scutari (2010). The first example is about a small synthetic dataset from Lauritzen and Spiegelhalter (1988) about lung diseases (tuberculosis, lung cancer or bronchitis) and visits to Asia.

First thing first, one need to precompute a cache of scores. We use the R package `abn` to do it.

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@@ -264,7 +264,7 @@ The distribution Q have to be smart. Closer it is from the posterior faster will

### Priors

Three priors are implemented in mcmcabn R package. The parameter `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, called Koivisto 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 $|G_n|$ is proportional to 1/[N-1 choose |G|] where there are N nodes in total.

Three priors are implemented in `mcmcabn` R package. The parameter `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, called Koivisto 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 $|G_n|$ is proportional to 1/[N-1 choose |G|] where there are N nodes in total.

Explicitly, the Koivisto prior is given by

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@@ -299,3 +299,4 @@ In statistical physics, in a Gibbs distribution the hyperparameter $\lambda$ is

| Koivisto, M. V. (2004). Exact Structure Discovery in Bayesian Networks, Journal of Machine Learning Research, vol 5, 549-573.

| Werhli, A. V., & Husmeier, D. (2007). "Reconstructing gene regulatory networks with Bayesian networks by combining expression data with multiple sources of prior knowledge". Statistical Applications in Genetics and Molecular Biology, 6 (Article 15).

| Imoto, S., Higuchi, T., Goto, T., Tashiro, K., Kuhara, S., & Miyano, S. (2003). Using Bayesian networks for estimating gene networks from microarrays and biological knowledge. In Proceedings of the European Conference on Computational Biology.

| 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.