  Model comparison for the purposes of selection, averaging and validation is a
problem found throughout statistics. Within the Bayesian paradigm, these
problems all require the calculation of the posterior probabilities of models
within a particular class. Substantial progress has been made in recent years,
but difficulties remain in the implementation of existing schemes. This paper
presents adaptive sequential Monte Carlo (\smc) sampling strategies to
characterise the posterior distribution of a collection of models, as well as
the parameters of those models. Both a simple product estimator and a
combination of \smc and a path sampling estimator are considered and existing
theoretical results are extended to include the path sampling variant. A novel
approach to the automatic specification of distributions within \smc algorithms
is presented and shown to outperform the state of the art in this area. The
performance of the proposed strategies is demonstrated via an extensive
empirical study. Comparisons with state of the art algorithms show that the
proposed algorithms are always competitive, and often substantially superior to
alternative techniques, at equal computational cost and considerably less
application-specific implementation effort.
