Abdelaati Daouia and Gilles Stupfler’s contribution to the Discussion of the ‘Discussion Meeting on the Analysis of citizen science data’
本文对Koh和Opitz的时空贝叶斯模型提出补充，建议用前沿分析方法估计鸟类首次到达日期，避免复杂贝叶斯结构，并融入空间位置和生态协变量以得到更平滑的预测。
We congratulate Jonathan Koh and Thomas Opitz for developing a sophisticated but fully operational spatiotemporal Bayesian hierarchical model for an explicit bias-corrected estimation of arrival dates from combined heterogeneous datasets. An econometrician may have thought, however, that this problem also belongs to the area of (frequentist) frontier analysis, which provides a rather different, and, we hope, useful perspective. More precisely, for a given species of birds and each pixel of a spatial mesh covering the study area, let Y represent the arrival date reported by an observer and T be the corresponding year of observation. As highlighted in the paper, the conditional distribution of Y given T obviously has a tail bounded to the left. The finite lower extremity of the support of Y given T=t defines the frontier point that corresponds to the population left-endpoint of all dates of occurrence of the species during the year t. This frontier function of t can be estimated by a global envelopment spline smoother under/without shape (e.g. concavity) constraints with automatic selection information criteria of the number and location of knots (Daouia et al., 2016), or by a local polynomial approach based on local extreme value statistics with adaptive selection of the tuning parameters (Jirak et al., 2014). Both approaches are based on the characterization of the yearly first arrival dates as a regression function in a nonparametric regression model with one-sided errors. The resulting spline or local polynomial boundary would then describe the yearly evolution of the desired first arrival date at the local zone considered. This avoids setting up a complex Bayesian hierarchical structure, as well as the Generalized Extreme Value approach whose goodness-of-fit to the data is not always easy to assess. Furthermore, instead of restricting the analysis to each pixel, thus resulting in a discrete geographical differentiation of the first arrival date, we suggest using all the data covering the study area and incorporating the observation location (i.e. longitude and latitude), as well as exogenous climate, land cover and other ecological factors into the estimation procedure as covariates (Wang et al., 2020), which would provide spatially smoother predictions of the true first arrivals. Proceeding in this way would also implicitly integrate the sampling effort, reflected by both preference and activity dimensions, as this would naturally show up in the confidence intervals, whether produced by asymptotics or bootstrapping. We think that this would be a useful complement to the very interesting approach constructed here. This research was supported by the French National Research Agency under the grants ANR-19-CE40-0013 (ExtremReg project), ANR-23-CE40-0009 (EXSTA project), ANR-17-EURE-0010 (EUR CHESS) and ANR-11-LABX-0020-01 (Centre Henri Lebesgue). A. Daouia and G. Stupfler acknowledge financial support from the TSE-HEC ACPR Chair “Regulation and systemic risks”. G. Stupfler acknowledges further support from the Chair Stress Test, RISK Management and Financial Steering of the Foundation Ecole Polytechnique.