Recent research has seen an increasingly fertile convergence of ideas from machine learning and formal modelling. Here we review some recently introduced methodologies for model checking and system design/parameter synthesis for logical properties against stochastic dynamical models. The crucial insight is a regularity result which states that the satisfaction probability of a logical formula is a smooth function of the parameters of a CTMC. This enables us to select an appropriate class of functional priors for Bayesian model checking and system design. We give a tutorial introduction to the statistical concepts, as well as an illustrative case study which demonstrates the usage of a newly-released software tool, U-check, which implements these methodologies.