# bf: Bayes factor between two graphs In BDgraph: Bayesian Structure Learning in Graphical Models using Birth-Death MCMC

## Description

Compute the Bayes factor between the structure of two graphs.

## Usage

 ```1 2``` ``` bf( num, den, bdgraph.obj, log = TRUE ) ```

## Arguments

 ```num, den``` An adjacency matrix corresponding to the true graph structure in which a_{ij}=1 if there is a link between notes i and j, otherwise a_{ij}=0. It can be an object with `S3` class `"graph"` from function `graph.sim`. It can be an object with `S3` class `"sim"` from function `bdgraph.sim`. `bdgraph.obj` An object of `S3` class `"bdgraph"`, from function `bdgraph`. It also can be an object of `S3` class `"ssgraph"`, from the function `ssgraph::ssgraph()` of `R` package `ssgraph::ssgraph()`. `log` A character value. If TRUE the Bayes factor is given as log(BF).

## Value

A single numeric value, the Bayes factor of the two graph structures `num` and `den`.

## References

Mohammadi, R. and Wit, E. C. (2019). BDgraph: An `R` Package for Bayesian Structure Learning in Graphical Models, Journal of Statistical Software, 89(3):1-30

Mohammadi, A. and Wit, E. C. (2015). Bayesian Structure Learning in Sparse Gaussian Graphical Models, Bayesian Analysis, 10(1):109-138

Mohammadi, A. et al (2017). Bayesian modelling of Dupuytren disease by using Gaussian copula graphical models, Journal of the Royal Statistical Society: Series C, 66(3):629-645

Letac, G., Massam, H. and Mohammadi, R. (2018). The Ratio of Normalizing Constants for Bayesian Graphical Gaussian Model Selection, arXiv preprint arXiv:1706.04416v2

Dobra, A. and Mohammadi, R. (2018). Loglinear Model Selection and Human Mobility, Annals of Applied Statistics, 12(2):815-845

`bdgraph`, `bdgraph.mpl`, `compare`, `bdgraph.sim`
 ``` 1 2 3 4 5 6 7 8 9 10 11 12 13``` ``` ## Not run: # Generating multivariate normal data from a 'circle' graph data.sim <- bdgraph.sim( n = 50, p = 6, graph = "circle", vis = TRUE ) # Running sampling algorithm bdgraph.obj <- bdgraph( data = data.sim ) graph_1 <- graph.sim( p = 6, vis = TRUE ) graph_2 <- graph.sim( p = 6, vis = TRUE ) bf( num = graph_1, den = graph_2, bdgraph.obj = bdgraph.obj ) ## End(Not run) ```