Given a sample of a Poisson point process with intensity $\lambda_f(x,y) = n \mathbf{1}(f(x) \leq y),$ we study recovery of the boundary function $f$ from a nonparametric Bayes perspective. Because of the irregularity of this model, the analysis is non-standard. We establish a general result for the posterior contraction rate with respect to the $L^1$-norm based on entropy and one-sided small probability bounds. From this, specific posterior contraction results are derived for Gaussian process priors and priors based on random wavelet series.

中文翻译：

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支撑边界恢复的后收缩率

给定强度为 $\lambda_f(x,y) = n \mathbf{1}(f(x) \leq y) 的泊松点过程的样本，我们研究从非参数贝叶斯中恢复边界函数 $f$看法。由于该模型不规范，分析不规范。我们基于熵和单边小概率边界建立了关于 $L^1$-范数的后收缩率的一般结果。由此，基于随机小波序列的高斯过程先验和先验导出了特定的后收缩结果。