Structural Bayesian Vector Autoregression

3

Super helpful, thank you (and for the very prompt reply!)

So, if I’ve understood correctly, to implement the equivalent of the a.mat and b.mat from this example:

# a.mat
##      [,1] [,2] [,3]
## [1,]   NA    0    0
## [2,]   NA   NA    0
## [3,]   NA   NA   NA
# b.mat
##      [,1] [,2] [,3]
## [1,]   NA    0    0
## [2,]    0   NA    0
## [3,]    0    0   NA

The lines in your first example one would have to change would be:

    state_chol, _, _ = pm.LKJCholeskyCov(
        "state_chol", eta=1, n=bvar_mod.k_posdef, sd_dist=pm.Exponential.dist(lam=1)
    )

    ar_params = pm.Normal("ar_params", mu=0, sigma=1, dims=ar_dims)
    state_cov = pm.Deterministic("state_cov", state_chol @ state_chol.T, dims=state_cov_dims)

Am I right in saying that a.mat is ar_params and b.mat is state_cov in your example? And apologies if this is a stupid question, but how do you modify the pm.Normal and pm.Deterministic lines to implement matrix structures with zeros in the right places?