PoissonRatioUQ: An R package for band ratio uncertainty quantification

We introduce an R package for Bayesian modeling and uncertainty quantification for problems involving count ratios. The modeling relies on the assumption that the quantity of interest is the ratio of Poisson means rather than the ratio of counts. We provide multiple different options for retrieval of this quantity for problems with and without spatial information included. Some added capability for uncertainty quantification for problems of the form $Z=(mT+z_0)^{p}$, where $Z$ is the intensity ratio and $T$ the quantity of interest, is included.

💡 Research Summary

The manuscript presents PoissonRatioUQ, an R package designed for Bayesian inference and uncertainty quantification (UQ) of count‑ratio problems where the quantity of interest is defined as the ratio of Poisson means rather than the raw count ratio. The authors argue that many remote‑sensing, atmospheric, and X‑ray astronomy applications implicitly treat observed photon counts in different spectral bands as direct ratios, which neglects the latent nature of the underlying Poisson intensities. By modeling the ratio of the latent means, the approach yields a principled hierarchical Bayesian framework that naturally propagates measurement noise and prior information.

The statistical core of the package is the Permanental Process, a type of Poisson point process whose intensity function is the half‑sum of squares of two independent Gaussian processes: λ(s)=½