Thanks Frank!
I should add that it is quite easy to do Bayesian and penalized-likelihood analyses with ordinary software by coding the priors as simple data records and adding them to the actual-data set. This data-augmentation (DA) method can be automated with simple commands. Evaluated relative to posterior sampling, DA runs fast, converges reliably, and provides accurate results.
An overview of DA with software illustrations for logistic risk, log-linear rate, and proportional hazards models is
Sullivan SG, Greenland S (2013) Bayesian regression in SAS software. Int J Epidemiol 42:308-17. doi:10.1093/ije/dys213
Important Erratum (2014) Int J Epidemiol 43:1667–1668,
Its use in bias analysis is illustrated in the Greenland 2009 paper cited above.
In my view, an important advantage of DA is this: By translating priors into equivalent data, it shows how much information the prior distributions is adding to the actual-data information. One can then see that many “skeptical” priors proposed and used in the medical literature are equivalent to far more information than is actually available in the application, and how such priors overwhelm the actual-data information. Thus the DA approach alerts one to “tune down” such priors to contextually reasonable levels.
DA also serves as a cross-check for both ordinary maximum-likelihood and posterior-sampling analyses, which can suffer convergence problems that go undetected by software and users (as illustrated in the Greenland-Mansournia-Altman 2016 paper cited above).