  Determining the best model or models for a particular data set, a process
known as Bayesian model comparison, is a critical part of probabilistic
inference. Typically, this process assumes a fixed model-space (that is, a
fixed set of candidate models). However, it is also possible to perform
Bayesian inference over model-spaces themselves, thus determining which spaces
provide the best explanation for observed data. Model-space inference (MSI)
allows the effective exclusion of poorly performing models (a process analogous
to Automatic Relevance Detection), and thus mitigates against the well-known
phenomenon of model dilution, resulting in posterior probability estimates that
are, on average, more accurate than those produced when using a fixed
model-space. We focus on model comparison in the context of multiple
independent data sets (as produced, for example, by multi-subject behavioural
or neuroimaging studies), and cast our proposal as a development of
random-effects Bayesian Model Selection, the current state-of-the-art in the
field. We demonstrate the increased accuracy of MSI using simulated behavioural
and neuroimaging data, as well as by assessing predictive performance in
previously-acquired empirical data. Additionally, we explore other applications
of MSI, including formal testing for a diversity of models within a population,
and comparison of model-spaces between populations. Our approach thus provides
an important new tool for model comparison.

Quantitative Methods