**BCDAG** (**B**ayesian **C**ausal **DAG**) is a package for Bayesian DAG structure learning and causal effect estimation from observational Gaussian data.

The methodology implemented has been presented in Castelletti, F. & Mascaro, A. (2021). *Structural learning and estimation of joint causal effects among network-dependent variables*, Statistical Methods & Applications, 1-26

The package can be installed executing the following chunk of code:

The workflow of the package consists of two sequential steps: causal structure learning, performed through the function `learn_DAG()`

and causal effect estimation, performed through the function `get_causaleffect()`

. For a more detailed description of the inner mechanisms of these two functions, we refer the reader to the vignettes.

Before using the two main functions of the package, we generate some data:

```
library(BCDAG)
# Randomly generate a DAG and the DAG-parameters
q = 8
w = 0.2
set.seed(123)
DAG = rDAG(q = q, w = w)
outDL = rDAGWishart(n = 1, DAG = DAG, a = q, U = diag(1, q))
L = outDL$L; D = outDL$D
Sigma = solve(t(L))%*%D%*%solve(L)
n = 200
# Generate observations from a Gaussian DAG-model
X = mvtnorm::rmvnorm(n = n, sigma = Sigma)
```

We can use the function `learn_DAG()`

to perform causal structure learning from the generated observational dataset:

Next, we can compute the BMA estimate of the causal effect on a response variable consequent to a hard intervention on a set of nodes by using `get_causaleffect()`

:

```
# the causal effect on node 1 of an intervention on {3,4}
out |>
get_causaleffect(targets = c(3,4), response = 1, BMA = TRUE)
```

The three steps here implemented are detailed in the vignettes 1 - Random data generation from Gaussian DAG-models, 2 - MCMC scheme for posterior inference of Gaussian DAG models: the `learn_DAG()`

function and 3 - Elaborate on the output of `learn_DAG()`

using get_ functions

- Alessandro Mascaro, Department of Economics, Management and Statistics, University of Milano-Bicocca, Milan, a.mascaro3@campus.unimib.it
- Federico Castelletti, Department of Statistical sciences, Università Cattolica del Sacro Cuore, Milan, federico.castelletti@unicatt.it