  In recent years, Bayesian methods have been proposed as a solution to a wide
range of issues in quantum state and process tomography. State-of-the-art
Bayesian tomography solutions suffer from three problems: numerical
intractability, a lack of informative prior distributions, and an inability to
track time-dependent processes. Here, we address all three problems. First, we
use modern statistical methods, as pioneered by Husz\'ar and Houlsby and by
Ferrie, to make Bayesian tomography numerically tractable. Our approach allows
for practical computation of Bayesian point and region estimators for quantum
states and channels. Second, we propose the first priors on quantum states and
channels that allow for including useful experimental insight. Finally, we
develop a method that allows tracking of time-dependent states and estimates
the drift and diffusion processes affecting a state. We provide source code and
animated visual examples for our methods.
