标题： 区域选择后的推理 显示英文标题

标题： Inference post region selection

摘要： 事后选择推断包括基于数据集提供统计保证，这些保证对同一数据集上的先验模型选择步骤具有鲁棒性。 本文研究了事后选择推断问题的一个实例，其中模型选择步骤是选择空间域中的一个矩形区域。 然后推断步骤包括构建该区域平均信号的置信区间。 这受到遗传学或脑成像等应用的推动。 我们的置信区间在一维情况下构建，然后推广到更高维度。 它们基于将所有可能的选择区域映射到其对应平均信号估计误差的过程。 我们证明了此过程在函数上收敛于具有明确协方差的极限高斯过程。 这使我们能够提供具有渐近保证的置信区间。 在使用模拟数据的数值实验中，我们表明对于小到中等规模的数据集，我们的覆盖率比例已接近名义水平。 我们还展示了不同噪声分布的影响以及我们的区间的鲁棒性。 最后，我们通过癌症学中DNA拷贝数数据分析的分割问题来展示我们方法的相关性。 显示英文摘要

摘要： Post-selection inference consists in providing statistical guarantees, based on a data set, that are robust to a prior model selection step on the same data set. In this paper, we address an instance of the post-selection-inference problem, where the model selection step consists in selecting a rectangular region in a spatial domain. The inference step then consists in constructing confidence intervals on the average signal of this region. This is motivated by applications such as genetics or brain imaging. Our confidence intervals are constructed in dimension one, and then extended to higher dimension. They are based on the process mapping all possible selected regions to their corresponding estimation errors on the average signal. We prove the functional convergence of this process to a limiting Gaussian process with explicit covariance. This enables us to provide confidence intervals with asymptotic guarantees. In numerical experiments with simulated data, we show that our coverage proportions are fairly close to the nominal level already for small to moderate data-set size. We also highlight the impact of various possible noise distributions and the robustness of our intervals. Finally, we illustrate the relevance of our method to a segmentation problem inspired by the analysis of DNA copy number data in cancerology.