  We present the first fully variational Bayesian inference scheme for
continuous Gaussian-process-modulated Poisson processes. Such point processes
are used in a variety of domains, including neuroscience, geo-statistics and
astronomy, but their use is hindered by the computational cost of existing
inference schemes. Our scheme: requires no discretisation of the domain; scales
linearly in the number of observed events; and is many orders of magnitude
faster than previous sampling based approaches. The resulting algorithm is
shown to outperform standard methods on synthetic examples, coal mining
disaster data and in the prediction of Malaria incidences in Kenya.
