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Determining the best model or models for a particular data set, a processknown as Bayesian model comparison, is a critical part of probabilisticinference. Typically, this process assumes a fixed model-space (that is, afixed set of candidate models). However, it is also possible to performBayesian inference over model-spaces themselves, thus determining which spacesprovide the best explanation for observed data. Model-space inference (MSI)allows the effective exclusion of poorly performing models (a process analogousto Automatic Relevance Detection), and thus mitigates against the well-knownphenomenon of model dilution, resulting in posterior probability estimates thatare, on average, more accurate than those produced when using a fixedmodel-space. We focus on model comparison in the context of multipleindependent data sets (as produced, for example, by multi-subject behaviouralor neuroimaging studies), and cast our proposal as a development ofrandom-effects Bayesian Model Selection, the current state-of-the-art in thefield. We demonstrate the increased accuracy of MSI using simulated behaviouraland neuroimaging data, as well as by assessing predictive performance inpreviously-acquired empirical data. Additionally, we explore other applicationsof MSI, including formal testing for a diversity of models within a population,and comparison of model-spaces between populations. Our approach thus providesan important new tool for model comparison.

Bayesian inference over model-spaces increases the accuracy of model  comparison and allows formal testing of hypotheses about model distributions  in experimental populations