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 towards 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, USA and the spatial distribution of Pacific silver firs in Findley Lake Reserve in Washington, USA highlight the usefulness of our scores for scientific model selection.
翻译:我们采用一类适当的评分规则,根据简要统计来评价空间点过程预测,这些评分规则依靠蒙特-卡洛对预期的近似值,因此可以很容易地评估任何可以模拟的点点过程模型。在这方面,它们比常用的对数分和其他现有的点进程预测的正确分数更为灵活。评分规则允许对点过程具体方面,如空间分布或集群趋势,对模型的校准进行评估。我们利用模拟分析我们的评分规则对预测的不同方面的敏感性,并将其与对数分进行比较。美国加利福尼亚北部地震发生时的应用和美国华盛顿Findley湖保护区太平洋银纤维的空间分布突出显示了我们的评分对科学模型选择的有用性。