  Bayesian analysis is a framework for parameter estimation that applies even
in uncertainty regimes where the commonly used local (frequentist) analysis
based on the Cram\'er-Rao bound is not well defined. In particular, it applies
when no initial information about the parameter value is available, e.g., when
few measurements are performed. Here, we consider three paradigmatic estimation
schemes in continuous-variable quantum metrology (estimation of displacements,
phases, and squeezing strengths) and analyse them from the Bayesian
perspective. For each of these scenarios, we investigate the precision
achievable with single-mode Gaussian states under homodyne and heterodyne
detection. This allows us to identify Bayesian estimation strategies that
combine good performance with the potential for straightforward experimental
realization in terms of Gaussian states and measurements. Our results provide
practical solutions for reaching uncertainties where local estimation
techniques apply, thus bridging the gap to regimes where asymptotically optimal
strategies can be employed.
