  The classic, two-component, crust-superfluid model of a neutron star can be
formulated as a noise-driven, linear dynamical system, in which the angular
velocities of the crust and superfluid are tracked using a Kalman filter
applied to electromagnetic pulse timing data and gravitational wave data, when
available. Here it is shown how to combine the marginal likelihood of the
Kalman filter and nested sampling to estimate full posterior distributions of
the six model parameters, extending previous analyses based on a
maximum-likelihood approach. The method is tested across an astrophysically
plausible parameter domain using Monte Carlo simulations. It recovers the
injected parameters to $\lesssim 10$ per cent for time series containing $\sim
10^3$ samples, typical of long-term pulsar timing campaigns. It runs
efficiently in $\mathcal O(1)$ CPU-hr for data sets of the above size. In a
present-day observational scenario, when electromagnetic data are available
only, the method accurately estimates three parameters: the relaxation time,
the ensemble-averaged spin-down of the system, and the amplitude of the
stochastic torques applied to the crust. In a future observational scenario,
where gravitational wave data are also available, the method also estimates the
ratio between the moments of inertia of the crust and the superfluid, the
amplitude of the stochastic torque applied to the superfluid, and the
crust-superfluid lag. These empirical results are consistent with a formal
identifiability analysis of the linear dynamical system.
