The `R`

package **BDgraph** provides statistical tools for Bayesian structure learning for undirected graphical models with *continuous*, *count*, *binary*, and *mixed data*. The package is implemented the recent improvements in the Bayesian graphical models’ literature, including Mohammadi and Wit (2015), Mohammadi et al. (2021), Mohammadi et al. (2017), and Dobra and Mohammadi (2018). Besides, the package contains several functions for simulation and visualization, as well as several multivariate datasets taken from the literature.

Install **BDgraph** using

`install.packages( "BDgraph" )`

First, we load **BDgraph** package as well as **pROC** and **ggplot2**

```
library( BDgraph )
library( pROC )
library( ggplot2 )
```

Here are two simple examples to show how to use the functionality of the package.

Here is a simple example to see the performance of the package for the Gaussian graphical models. First, by using the function `bdgraph.sim()`

, we simulate 200 observations (n = 200) from a multivariate Gaussian distribution with 15 variables (p = 15) and “scale-free” graph structure, as follows

```
set.seed( 20 )
= bdgraph.sim( n = 200, p = 15, graph = "scale-free", vis = TRUE ) data.sim
```

Since the generated data are Gaussian, we run the `bdgraph()`

function by choosing `method = "ggm"`

, as follows

`= bdgraph( data = data.sim, method = "ggm", iter = 5000, verbose = FALSE ) bdgraph.obj `

To report confusion matrix with cutoff point 0.5:

```
conf.mat( actual = data.sim, pred = bdgraph.obj, cutoff = 0.5 )
Actual0 1
Prediction 0 89 4
1 2 10
conf.mat.plot( actual = data.sim, pred = bdgraph.obj, cutoff = 0.5 )
```

To compare the result with the true graph

`compare( data.sim, bdgraph.obj, main = c( "Target", "BDgraph" ), vis = TRUE )`

```
Target BDgraph
true positive 14 10.000
true negative 91 89.000
false positive 0 2.000
false negative 0 4.000
F1-score 1 0.769
specificity 1 0.978
sensitivity 1 0.714
MCC 1 0.740
```

Now, as an alternative, we run the `bdgraph.mpl()`

function which is based on the GGMs and marginal pseudo-likelihood, as follows

```
= bdgraph.mpl( data = data.sim, method = "ggm", iter = 5000, verbose = FALSE )
bdgraph.mpl.obj
conf.mat( actual = data.sim, pred = bdgraph.mpl.obj )
Actual0 1
Prediction 0 89 4
1 2 10
conf.mat.plot( actual = data.sim, pred = bdgraph.mpl.obj )
```

We could compare the results of both algorithms with the true graph as follows

```
compare( data.sim, list( bdgraph.obj, bdgraph.mpl.obj ),
main = c( "Target", "BDgraph", "BDgraph.mpl" ), vis = TRUE )
```

```
Target BDgraph BDgraph.mpl
true positive 14 10.000 10.000
true negative 91 89.000 89.000
false positive 0 2.000 2.000
false negative 0 4.000 4.000
F1-score 1 0.769 0.769
specificity 1 0.978 0.978
sensitivity 1 0.714 0.714
MCC 1 0.740 0.740
```

To see the performance of the BDMCMC algorithm we could plot the ROC curve as follows

```
= BDgraph::roc( pred = bdgraph.obj, actual = data.sim )
roc.bdgraph = BDgraph::roc( pred = bdgraph.mpl.obj, actual = data.sim )
roc.bdgraph.mpl
::ggroc( list( BDgraph = roc.bdgraph, BDgraph.mpl = roc.bdgraph.mpl ), size = 0.8 ) +
pROCtheme_minimal() + ggtitle( "ROC plots with AUC" ) +
scale_color_manual( values = c( "red", "blue" ),
labels = c( paste( "AUC=", round( auc( roc.bdgraph ), 3 ), "; BDgraph; " ),
paste( "AUC=", round( auc( roc.bdgraph.mpl ), 3 ), "; BDgraph.mpl" ) ) ) +
theme( legend.title = element_blank() ) +
theme( legend.position = c( .7, .3 ), text = element_text( size = 17 ) ) +
geom_segment( aes( x = 1, xend = 0, y = 0, yend = 1 ), color = "grey", linetype = "dashed" )
```

Here is a simple example to see the performance of the package for the mixed data using Gaussian copula graphical models. First, by using the function `bdgraph.sim()`

, we simulate 300 observations (n = 300) from mixed data (`type = "mixed"`

) with 10 variables (p = 10) and “random” graph structure, as follows

```
set.seed( 2 )
= bdgraph.sim( n = 300, p = 10, type = "mixed", graph = "random", vis = TRUE ) data.sim
```

Since the generated data are mixed data, we are using run the `bdgraph()`

function by choosing `method = "gcgm"`

, as follows:

`= bdgraph( data = data.sim, method = "gcgm", iter = 5000, verbose = FALSE ) bdgraph.obj `

To compare the result with the true graph, we could run

`compare( data.sim, bdgraph.obj, main = c( "Target", "BDgraph" ), vis = TRUE )`

```
Target BDgraph
true positive 12 9.000
true negative 33 29.000
false positive 0 4.000
false negative 0 3.000
F1-score 1 0.720
specificity 1 0.879
sensitivity 1 0.750
MCC 1 0.613
```

For more examples see Mohammadi and Wit (2019).