gIVBMA.jl

Bayesian Model Averaging in Instrumental Variable Models. This package implements the gIVBMA method proposed in Steiner and Steel (2025).

Installation

The package is not yet available from the general registry, but can be installed directly from GitHub:

using Pkg; Pkg.add(url="https://github.com/gregorsteiner/gIVBMA.jl.git")

Usage

The main function is givbma which requires an outcome vector y, a matrix of endogenous variables X, a matrix of potential instruments Z, and a matrix of potential (exogenous) covariates W:

fit = givbma(y, X, Z, W)

will return a GIVBMA object containing a posterior sample of the model parameters averaged over the outcome and treatment models, the visited outcome and treatment models, and the input data. Alternatively, one can only specify a matrix Z of potential instruments and covariates:

fit = givbma(y, X, Z)

which allows all columns of Z to be included in the outcome and treatment model. Note that an intercept is automatically included and there is no need to include it in either X, W, or Z. The optional keyword arguments are:

• iter: the number of iterations.
• burn: the number of iterations discarded as burn-in; the function returns iter-burn posterior samples.
• dist: a vector of distributions of the outcome and the endogenous variables (defaults to Gaussian). Currently, we support "Gaussian", "PLN" (Poisson-Log-Normal), and "BL" (Beta-Logistic).
• g_prior: the choice of the g hyperparameter. Currently, we support "BRIC" (default) and "hyper-g/n".
• two_comp: a Boolean indicating whether the two-component g-prior should be used in the treatment model (defaults to false). The two-component prior can only be used with a single endogenous variable (i.e. X only has a single column).
• ν: the degrees of freedom parameter for the inverse Wishart prior on the covariance matrix. If not specified, this defaults to an Exponential hyperprior.
• m: the prior mean model size. If not specified, it defaults to k/2 in the outcome model and (k+p)/2 in the treatment model, where k is the number of exogenous covariates and p is the number of instruments.
• r_prior: a Distribution object specifying the prior on additional parameters for any non-Gaussian distributions involved. Currently, this only includes the dispersion parameter of the Beta-Logistic distribution (which defaults to an Exponential with scale 1).

A useful function is rbw:

posterior = rbw(fit)

which returns a vector of Distribution objects containing Rao-Blackwellized estimates of the marginal posterior distributions of each component of the treatment effect vector. This can be used to extract summary statistics or plot the marginal posterior distribution:

# Extract a vector of posterior means or medians
map(mean, posterior)
map(median, posterior)

# Plot the posterior distribution corresponding to the first column of X
using CairoMakie
lines(posterior[1])

References

Steiner, G. and Steel, M. (2025). Bayesian Model Averaging in Causal Instrumental Variable Models. arXiv:2504.13520