PoissonRatioUQ: An R package for band ratio uncertainty quantification
Pith reviewed 2026-05-16 06:58 UTC · model grok-4.3
The pith
An R package performs Bayesian inference on the ratio of Poisson means to quantify uncertainty in count data problems.
A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.
Core claim
The PoissonRatioUQ package implements Bayesian methods to estimate the ratio of Poisson means and to obtain associated posterior uncertainty measures, with dedicated options for problems that include spatial information and with added capability for uncertainty quantification on transformed intensity ratios of the form Z equals (mT plus z0) to the power p.
What carries the argument
The PoissonRatioUQ R package, which carries out Bayesian inference directly on the ratio of two Poisson means and supplies retrieval routines for both spatial and non-spatial settings.
If this is right
- Posterior samples and credible intervals become available for the ratio parameter in standard count-ratio problems.
- Spatial dependence structures can be incorporated when the counts exhibit spatial correlation.
- Uncertainty intervals can be obtained for derived quantities that follow the power-law form Z equals (mT plus z0) to the power p.
- Multiple modeling options allow users to select the retrieval method best matched to the presence or absence of spatial information.
Where Pith is reading between the lines
- In fields that routinely form ratios from Poisson counts, such as remote sensing or particle counting, the package supplies a ready route to calibrated posterior uncertainty.
- The modeling framework could be extended to hierarchical settings where multiple ratios share common hyperparameters.
- Integration with existing R spatial packages would let users combine the ratio inference with geostatistical tools for more complex data sets.
Load-bearing premise
The quantity of interest is the ratio of the Poisson means themselves rather than the ratio of the observed counts.
What would settle it
Generate synthetic count pairs from two Poisson distributions whose mean ratio is known exactly, run the package to obtain credible intervals for that ratio, and check whether the intervals contain the true value at the advertised coverage rate.
Figures
read the original abstract
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.
Editorial analysis
A structured set of objections, weighed in public.
Referee Report
Summary. The manuscript introduces the R package PoissonRatioUQ for Bayesian modeling and uncertainty quantification of count ratios. The central modeling choice is to treat the quantity of interest as the ratio of Poisson means (rather than the ratio of observed counts). The package supplies multiple retrieval options for this ratio in both non-spatial and spatially informed settings and adds support for uncertainty quantification on transformed quantities of the form Z = (mT + z0)^p.
Significance. If the implementation is correct and accompanied by adequate validation, the package would supply a practical, open-source tool for rigorous uncertainty propagation in Poisson-ratio problems that arise in astronomy, ecology, and particle physics. The explicit statement of the Poisson-mean-ratio assumption and the inclusion of both spatial and power-law extensions are positive features for applied users.
major comments (2)
- [Abstract and package description] The manuscript provides no simulation studies, coverage checks, or comparisons against existing Poisson-ratio estimators (e.g., the delta method or profile-likelihood approaches). Without such evidence it is impossible to verify that the Bayesian implementation recovers the claimed uncertainty quantification.
- [Methods and implementation sections] No details are given on prior specifications, MCMC sampler, convergence diagnostics, or effective sample sizes. These choices are load-bearing for any Bayesian UQ claim and must be documented before the package can be recommended for production use.
minor comments (1)
- [Title and Abstract] The abstract and title use the term 'band ratio' without defining it; a brief clarification in the introduction would help readers outside the immediate application domain.
Simulated Author's Rebuttal
We thank the referee for their constructive comments on the PoissonRatioUQ manuscript. We address each major point below and will revise the manuscript to incorporate the requested additions.
read point-by-point responses
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Referee: The manuscript provides no simulation studies, coverage checks, or comparisons against existing Poisson-ratio estimators (e.g., the delta method or profile-likelihood approaches). Without such evidence it is impossible to verify that the Bayesian implementation recovers the claimed uncertainty quantification.
Authors: We agree that simulation studies and comparisons are needed to substantiate the uncertainty quantification claims. The current manuscript emphasizes package functionality and modeling assumptions rather than exhaustive validation. In the revised version we will add a dedicated simulation section that reports coverage properties of the Bayesian credible intervals for the Poisson mean ratio under both non-spatial and spatial settings, together with direct numerical comparisons against the delta method and profile-likelihood estimators. revision: yes
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Referee: No details are given on prior specifications, MCMC sampler, convergence diagnostics, or effective sample sizes. These choices are load-bearing for any Bayesian UQ claim and must be documented before the package can be recommended for production use.
Authors: Implementation details currently reside in the package source and vignettes. We accept that the manuscript should summarize these choices explicitly. The revision will include a concise methods subsection stating the default weakly informative Gamma priors on the Poisson rates, the use of Hamiltonian Monte Carlo sampling (via Stan), and recommended convergence diagnostics (R-hat statistics and effective sample sizes), together with example code for users to inspect these quantities. revision: yes
Circularity Check
No significant circularity
full rationale
The paper is a software contribution describing an R package for Bayesian inference on ratios of Poisson means (with spatial and power-law extensions). The central modeling choice is presented explicitly as an assumption rather than derived from prior results or self-citations. No equations, fitted parameters, or uniqueness claims are shown that reduce by construction to the paper's own inputs. The work contains no load-bearing self-citation chains or ansatzes smuggled via prior author work. This is a standard, self-contained software release with no internal derivation that collapses to its own definitions.
Axiom & Free-Parameter Ledger
axioms (1)
- domain assumption The quantity of interest is the ratio of Poisson means rather than the ratio of counts.
discussion (0)
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