Abstract
Given a sample of a Poisson point process with intensity
λf(x,y)=n1(f(x)≤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 L1-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.
λf(x,y)=n1(f(x)≤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 L1-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.
| Original language | English |
|---|---|
| Pages (from-to) | 6638 |
| Number of pages | 6656 |
| Journal | Stochastic processes and their applications |
| Volume | 130 |
| Issue number | 11 |
| DOIs | |
| Publication status | Published - 1 Nov 2020 |
Keywords
- UT-Hybrid-D
- Posterior contraction
- Poisson point process
- Boundary detection
- Gaussian prior
- Wavelet prior
- Frequentist Bayesian analysis
- 22/2 OA procedure