I am trying to estimate a regression model with several covariates where several of the covariates have a different amount of history. Any advice on how to set this problem up is appreciated.
Hi @mlemmon, could you please provide a bit more details of what you are trying to do? Preferabily with some data 
As @junpenglao suggested in another thread, you can feed in the entire history, then have PyMC3 handle the missing values.
See https://github.com/pymc-devs/pymc3/blob/master/pymc3/examples/lasso_missing.py4