This might be a good place to not that full Bayesianism is getting easier to practice in statistics. Doing fully Bayesian analysis has been tough for many models because it's computationally difficult since standard MCMC methods often don't scale that well, so you can only fit models with few parameters.

However, there are at least two statistical libraries STAN and PyMC3 (which I help out with) which implement Hamiltonian Monte Carlo (which scales well) and provide an easy language for model building. This allows you to fit relatively complex models, without thinking too much about how to do it.

Join the revolution!