  Now over 20 years old, functional MRI (fMRI) has a large and growing
literature that is best synthesised with meta-analytic tools. As most authors
do not share image data, only the peak activation coordinates (foci) reported
in the paper are available for Coordinate-based Meta-analysis (CBMA).
Neuroimaging meta-analysis is used to 1) identify areas of consistent
activation; and 2) build a predictive model of task type or cognitive process
for new studies (reverse inference). To simultaneously address these aims, we
propose a Bayesian point process hierarchical model for CBMA. We model the foci
from each study as a doubly stochastic Poisson process, where the
study-specific log intensity function is characterised as a linear combination
of a high-dimensional basis set. A sparse representation of the intensities is
guaranteed through latent factor modeling of the basis coefficients. Within our
framework, it is also possible to account for the effect of study-level
covariates (meta-regression), significantly expanding the capabilities of the
current neuroimaging meta-analysis methods available. We apply our methodology
to synthetic data and a neuroimaging meta-analysis dataset.
