  We consider Bayesian inference from multiple time series described by a
common state-space model (SSM) structure, but where different subsets of
parameters are shared between different submodels. An important example is
disease-dynamics, where parameters can be either disease or location specific.
Parameter inference in these models can be improved by systematically
aggregating information from the different time series, most notably for short
series. Particle Gibbs (PG) samplers are an efficient class of algorithms for
inference in SSMs, in particular when conjugacy can be exploited to marginalize
out model parameters from the state update. We present two different PG
samplers that marginalize static model parameters on-the-fly: one that updates
one model at a time conditioned on the datasets for the other models, and one
that concurrently updates all models by stacking them into a high-dimensional
SSM. The distinctive features of each sampler make them suitable for different
modelling contexts. We provide insights on when each sampler should be used and
show that they can be combined to form an efficient PG sampler for a model with
strong dependencies between states and parameters. The performance is
illustrated on two linear-Gaussian examples and on a real-world example on the
spread of mosquito-borne diseases.
