Sensing Cox Processes via Posterior Sampling and Positive Bases
This work addresses adaptive sensing problems in spatial statistics, such as environmental monitoring and crime modeling, but appears incremental as it builds on existing posterior sampling methods with a new basis representation.
The paper tackles adaptive sensing of Cox point processes by introducing tasks like maximizing captured events and learning intensity function level sets, and demonstrates the approach with examples from environmental monitoring and crime rate modeling, showing comparisons to classical Bayesian experimental design.
We study adaptive sensing of Cox point processes, a widely used model from spatial statistics. We introduce three tasks: maximization of captured events, search for the maximum of the intensity function and learning level sets of the intensity function. We model the intensity function as a sample from a truncated Gaussian process, represented in a specially constructed positive basis. In this basis, the positivity constraint on the intensity function has a simple form. We show how an minimal description positive basis can be adapted to the covariance kernel, non-stationarity and make connections to common positive bases from prior works. Our adaptive sensing algorithms use Langevin dynamics and are based on posterior sampling (\textsc{Cox-Thompson}) and top-two posterior sampling (\textsc{Top2}) principles. With latter, the difference between samples serves as a surrogate to the uncertainty. We demonstrate the approach using examples from environmental monitoring and crime rate modeling, and compare it to the classical Bayesian experimental design approach.