Validation of point process predictions with proper scoring rules

We introduce a class of proper scoring rules for evaluating spatial point process forecastsbased on summary statistics. These scoring rules rely on Monte-Carlo approximation ofan expectation and can therefore easily be evaluated for any point process model that canbe simulated. In this regard, they are more flexible than the commonly used logarithmicscore; they are also fruitful for evaluating the calibration of a model to specific aspectsof a point process, such as its spatial distribution or tendency towards clustering. Weshow using simulations that our scoring rules are able to discern between competingmodels better than the logarithmic score. An application on growth in Pacific silver firtrees demonstrates the promise of our scores for scientific model selection.