  A new discrete-time shot noise Cox process for spatiotemporal data is
proposed. The random intensity is driven by a dependent sequence of latent
gamma random measures. Some properties of the latent process are derived, such
as an autoregressive representation and the Laplace functional. Moreover, these
results are used to derive the moment, predictive, and pair correlation
measures of the proposed shot noise Cox process. The model is flexible but
still tractable and allows for capturing persistence, global trends, and latent
spatial and temporal factors. A Bayesian inference approach is adopted, and an
efficient Markov Chain Monte Carlo procedure based on conditional Sequential
Monte Carlo is proposed. An application to georeferenced wildfire data
illustrates the properties of the model and inference.
