Validation of point process predictions with proper scoring rules
提出一类基于汇总统计量的恰当评分规则，用于评估空间点过程预测，通过蒙特卡洛近似计算，比常用对数评分更灵活，能检验模型在空间分布或聚类倾向等方面的校准性，并应用于地震和树木分布数据。
Abstract We introduce a class of proper scoring rules for evaluating spatial point process forecasts based on summary statistics. These scoring rules rely on Monte Carlo approximations of expectations and can therefore easily be evaluated for any point process model that can be simulated. In this regard, they are more flexible than the commonly used logarithmic score and other existing proper scores for point process predictions. The scoring rules allow for evaluating the calibration of a model to specific aspects of a point process, such as its spatial distribution or tendency toward clustering. Using simulations, we analyze the sensitivity of our scoring rules to different aspects of the forecasts and compare it to the logarithmic score. Applications to earthquake occurrences in northern California, United States and the spatial distribution of Pacific silver firs in Findley Lake Reserve in Washington highlight the usefulness of our scores for scientific model selection.