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报告题目：Spatial statistics: testing hypothesis issues and forest statistics application

报告人：Prof. Pavel Grabarnik (俄罗斯科学院)

报告时间：2022年6月13日 4:00~5:30 下午 北京时间

报告地点：Zoom会议 会议号：943 6896 7554 密码：123456

报告摘要：Goodness-of-Fit tests as well as mark independence tests play a fundamental role in spatial statistics and modeling and have been thoroughly considered in the statistical literature. Nevertheless, some popular established tests are not fully satisfactory and need improvement. The present talk aims to contribute to this issue. A deviation test converts information on a functional summary statistic F(r) in a single number and compares it with some reference value, obtained from simulations of the model corresponding to the null hypothesis. In contrast, in an envelope test the values of F(r) are inspected for a range of distances simultaneously. Thus, statisticians are confronted in this case with the multiple testing problem. If F(r) were of interest only for a single distance, one could proceed as in the deviation test. However, single-distance tests are rarely applied, since prior knowledge of a single "ecologically interesting" distance r is untypical in practice. We show that the type I error probability, when testing over an interval of distances, exceeds that for individual scales heavily, and therefore, the conventional pointwise simulation envelope test cannot be recommended as a rigorous statistical tool. To overcome this drawback we propose the refined envelope test as a testing procedure where the type I error probability is evaluated by simulation and taken into account in making conclusions. In this way, it becomes a valuable tool both for statistical inference and for understanding the reasons of possible rejections of the independence hypothesis. We discuss in detail the use of deviation and refined simulation envelope tests for testing hypotheses of mark independence hypothesis. Some examples from forest ecology illustrate the application of both test types.

报告人简介：Pavel Grabarnik，1957年，教授，俄罗斯科学院。圣彼得堡国立理工大学应用统计副博士（1992年），彼得罗扎沃茨克国立大学博士（2013年）。研究方向为空间统计与生态建模。目前担任俄罗斯科学院“普希诺科学中心生物研究中心”联邦研究中心负责人（Director of the Federal Research Center “Puschino scientific Center for biological research of the Russian Academy of Sciences”），兼生态建模实验室主任（Head of the Laboratory of Ecological Modelling）。