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arxiv: 2602.07165 · v2 · submitted 2026-02-06 · 📊 stat.CO · physics.data-an· stat.ME

PoissonRatioUQ: An R package for band ratio uncertainty quantification

Matthew LeDuc , Tomoko Matsuo This is my paper

Pith reviewed 2026-05-16 06:58 UTC · model grok-4.3

classification 📊 stat.CO physics.data-anstat.ME
keywords R packageBayesian modelinguncertainty quantificationPoisson ratiocount dataspatial statistics
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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.

The paper presents an R package called PoissonRatioUQ for Bayesian modeling and uncertainty quantification involving ratios of counts. Its central modeling choice treats the quantity of interest as the ratio of the underlying Poisson means rather than the ratio of observed counts. The package supplies multiple retrieval options that handle both non-spatial and spatially structured data. It also adds support for propagating uncertainty through transformations of the form Z equals (mT plus z0) to the power p.

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

These are editorial extensions of the paper, not claims the author makes directly.

  • 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

Figures reproduced from arXiv: 2602.07165 by Matthew LeDuc, Tomoko Matsuo.

Figure 3.1
Figure 3.1. Figure 3.1: Example retrieval and timing study using the permanental process model to retrieve [PITH_FULL_IMAGE:figures/full_fig_p006_3_1.png] view at source ↗
Figure 3.2
Figure 3.2. Figure 3.2: Estimation results from two realizations of the Poisson data for the nonlinear trans [PITH_FULL_IMAGE:figures/full_fig_p007_3_2.png] view at source ↗
Figure 4.1
Figure 4.1. Figure 4.1: Comparison: Empirical distribution, CDF, and quantiles from [PITH_FULL_IMAGE:figures/full_fig_p009_4_1.png] view at source ↗
Figure 4.2
Figure 4.2. Figure 4.2: Demonstration of the algorithm for calculating the highest-posterior density sets on a [PITH_FULL_IMAGE:figures/full_fig_p014_4_2.png] view at source ↗
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.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

2 major / 1 minor

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)
  1. [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.
  2. [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)
  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

2 responses · 0 unresolved

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

  1. 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

  2. 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

0 steps flagged

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

0 free parameters · 1 axioms · 0 invented entities

The central modeling choice rests on treating the ratio of Poisson means as the target quantity; no free parameters or invented entities are mentioned in the abstract.

axioms (1)
  • domain assumption The quantity of interest is the ratio of Poisson means rather than the ratio of counts.
    Explicitly stated in the abstract as the foundation for the Bayesian modeling.

pith-pipeline@v0.9.0 · 5376 in / 1216 out tokens · 29511 ms · 2026-05-16T06:58:32.524300+00:00 · methodology

discussion (0)

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Reference graph

Works this paper leans on

35 extracted references · 35 canonical work pages

  1. [1]

    Thermospheric Composition and Solar EUV Flux From the Global-Scale Observations of the Limb and Disk (GOLD) Mission

    J. Correira et al. “Thermospheric Composition and Solar EUV Flux From the Global-Scale Observations of the Limb and Disk (GOLD) Mission”. In:Journal of Geophysical Research: Space Physics(2021).doi:https : / / doi . org / 10 . 1029 / 2021JA029517.url:https : //agupubs.onlinelibrary.wiley.com/doi/abs/10.1029/2021JA029517

    work page doi:10.1029/2021ja029517 2021

  2. [2]

    The Thermospheric Column O/N2 Ratio

    R. R. Meier. “The Thermospheric Column O/N2 Ratio”. In:Journal of Geophysical Re- search: Space Physics(2021).url:https://doi.org/10.1029/2020JA029059

    work page doi:10.1029/2020ja029059 2021

  3. [3]

    Satellite remote sensing of thermospheric O/N2 and solar EUV: 1. Theory

    D. J. Strickland, J. S. Evans, and L. J. Paxton. “Satellite remote sensing of thermospheric O/N2 and solar EUV: 1. Theory”. In:Journal of Geophysical Research: Space Physics(1995). url:https://doi.org/10.1029/95JA00574

    work page doi:10.1029/95ja00574 1995

  4. [4]

    O/N2 changes during 1–4 October 2002 storms: IMAGE SI-13 and TIMED/GUVI observations

    Y. Zhang et al. “O/N2 changes during 1–4 October 2002 storms: IMAGE SI-13 and TIMED/GUVI observations”. In:Journal of Geophysical Research: Space Physics(2004).doi:https : / / doi . org / 10 . 1029 / 2004JA010441.url:https : / / agupubs . onlinelibrary . wiley . com/doi/abs/10.1029/2004JA010441

    work page doi:10.1029/2004ja010441 2002

  5. [5]

    New approaches for quantifying and understanding thermosphere temper- ature variability from far ultraviolet dayglow

    Clayton Cantrall. “New approaches for quantifying and understanding thermosphere temper- ature variability from far ultraviolet dayglow”. PhD thesis. University of Colorado-Boulder, 2022

    work page 2022

  6. [6]

    Deriving column-integrated thermospheric tem- perature with the N2 Lyman–Birge–Hopfield (2,0) band

    Clayton Cantrall and Tomoko Matsuo. “Deriving column-integrated thermospheric tem- perature with the N2 Lyman–Birge–Hopfield (2,0) band”. In:Atmospheric Measurement Techniques(2021).doi:10.5194/amt-14-6917-2021

    work page doi:10.5194/amt-14-6917-2021 2021

  7. [7]

    2025.url:https://doi

    Matthew LeDuc, Tomoko Matsuo, and William Kleiber.A New Approach to Inversion of Multi-spectral Data and Applications to FUV Remote Sensing. 2025.url:https://doi. org/10.5194/EGUSPHERE-2025-5570

    work page doi:10.5194/egusphere-2025-5570 2025

  8. [8]

    Deriving Thermospheric Tem- perature From Observations by the Global Ultraviolet Imager on the Thermosphere Iono- sphere Mesosphere Energetics and Dynamics Satellite

    Yongliang Zhang, Larry J. Paxton, and Robert K. Schaefer. “Deriving Thermospheric Tem- perature From Observations by the Global Ultraviolet Imager on the Thermosphere Iono- sphere Mesosphere Energetics and Dynamics Satellite”. In:Journal of Geophysical Research: Space Physics(2019)

    work page 2019

  9. [9]

    Spatial analysis of the polycyclic aromatic hydrocarbon features southeast of the Orion Bar

    C Boersma, RH Rubin, and LJ Allamandola. “Spatial analysis of the polycyclic aromatic hydrocarbon features southeast of the Orion Bar”. In:The Astrophysical Journal(2012)

    work page 2012

  10. [10]

    Hardness Ratio estimation in Low Counting X-Ray Photometry

    Y.K. Jin, S.N. Zhang, and J.F. Wu. “Hardness Ratio estimation in Low Counting X-Ray Photometry”. In:The Astrophysical Journal(2006).doi:10.1086/508677

    work page doi:10.1086/508677 2006

  11. [11]

    Bayesian Estimation of Hardness Ratios: Modeling and Computa- tions

    Taeyoung Park et al. “Bayesian Estimation of Hardness Ratios: Modeling and Computa- tions”. In:The Astrophysical Journal(2006).doi:10.1086/507406.url:https://dx. doi.org/10.1086/507406

    work page doi:10.1086/507406.url:https://dx 2006

  12. [12]

    Analysis of bright source hardness ratios in the 4 yr Insight-HXMT galactic plane scanning survey catalog

    Chen Wang et al. “Analysis of bright source hardness ratios in the 4 yr Insight-HXMT galactic plane scanning survey catalog”. In:Research in Astronomy and Astrophysics(2024). 16

    work page 2024

  13. [13]

    Upper Atmosphere Radi- ance Data Assimilation: A Feasibility Study for GOLD Far Ultraviolet Observations

    Clayton E. Cantrall, Tomoko Matsuo, and Stanley C. Solomon. “Upper Atmosphere Radi- ance Data Assimilation: A Feasibility Study for GOLD Far Ultraviolet Observations”. In: Journal of Geophysical Research: Space Physics(2019).url:https://agupubs.onlinelibrary. wiley.com/doi/abs/10.1029/2019JA026910

    work page doi:10.1029/2019ja026910 2019

  14. [14]

    Statistical Bias in Isotope Ratios

    Christopher D. Coath, Robert C. J. Steele, and W. Fred Lunnon. “Statistical Bias in Isotope Ratios”. In:Journal of Analytical Atomic Spectrometry(2013)

    work page 2013

  15. [15]

    A Generalized Beta Prime Distribution as the Ratio Prob- ability Density Function for Change Detection Between Two SAR Intensity Images With Different Number of Looks

    Gerard Gallardo i Peres et al. “A Generalized Beta Prime Distribution as the Ratio Prob- ability Density Function for Change Detection Between Two SAR Intensity Images With Different Number of Looks”. In:IEEE Transactions on Geoscience and Remote Sensing (2024).doi:10.1109/TGRS.2024.3369509

    work page doi:10.1109/tgrs.2024.3369509 2024

  16. [16]

    Interstellar Dust Experiment (IDEX) onboard NASA’s Interstellar Mapping and Acceleration Probe (IMAP)

    Mih´ aly Hor´ anyi et al. “Interstellar Dust Experiment (IDEX) onboard NASA’s Interstellar Mapping and Acceleration Probe (IMAP)”. In:Space Science Reviews(2025)

    work page 2025

  17. [17]

    Atmospheric temperature measurements at altitudes of 5-30km with a double-grating-based pure rotational Raman lidar

    Jingyu Jia and Fan Yi. “Atmospheric temperature measurements at altitudes of 5-30km with a double-grating-based pure rotational Raman lidar”. In:Appl. Opt.(2014).doi:10.1364/ AO.53.005330.url:https://opg.optica.org/ao/abstract.cfm?URI=ao-53-24-5330

    work page 2014

  18. [18]

    Improving Solar Flare Now- casting with the Hot Onset Precursor Event Technique

    Anant Telikicherla, Thomas N Woods, and Bennet D Schwab. “Improving Solar Flare Now- casting with the Hot Onset Precursor Event Technique”. In:The Astrophysical Journal (2025)

    work page 2025

  19. [19]

    A new strategy for ionospheric remote sensing using the 130.4/135.6 nm airglow intensity ratios

    XiaoHan Yin, JianQi Qin, and Larry J. Paxton. “A new strategy for ionospheric remote sensing using the 130.4/135.6 nm airglow intensity ratios”. In:Earth and Planetary Physics (2023).doi:10.26464/epp2023042

    work page doi:10.26464/epp2023042 2023

  20. [20]

    The Permanental Process

    Peter McCullagh and Jesper Møller. “The Permanental Process”. In:Advances in Applied Probability(2006).url:https://doi.org/10.1017/S0001867800001361

    work page doi:10.1017/s0001867800001361 2006

  21. [21]

    Properties of spatial Cox process models

    Jesper Møller. “Properties of spatial Cox process models”. In:Journal of Statistical Research of Iran(2005)

    work page 2005

  22. [22]

    R Foundation for Statistical Computing

    R Core Team.R: A Language and Environment for Statistical Computing. R Foundation for Statistical Computing. Vienna, Austria, 2025.url:https://www.R-project.org/

    work page 2025

  23. [23]

    Streit.Poisson Point Processes:Imaging, Tracking, and Sensing

    Roy L. Streit.Poisson Point Processes:Imaging, Tracking, and Sensing. Springer, 2010

    work page 2010

  24. [24]

    Poisson intensity estimation with reproducing kernels

    Seth Flaxman, Yee Whye Teh, and Dino Sejdinovic. “Poisson intensity estimation with reproducing kernels”. In:Electronic Journal of Statistics(2017)

    work page 2017

  25. [25]

    Regularization and Approximation of Linear Operator Equations in Reproducing Kernel Spaces

    M.Z. Nashed and Grace Wahba. “Regularization and Approximation of Linear Operator Equations in Reproducing Kernel Spaces”. In:Bulletin of the American Mathematical Society (1974)

    work page 1974

  26. [26]

    Fast Bayesian Intensity Estimation for the Per- manental Process

    Christian J. Walder and Adrian N. Bishop. “Fast Bayesian Intensity Estimation for the Per- manental Process”. In:Proceedings of the 34th International Conference on Machine Learn- ing. Ed. by Doina Precup and Yee Whye Teh. Proceedings of Machine Learning Research. PMLR, 2017.url:https://proceedings.mlr.press/v70/walder17a.html

    work page 2017

  27. [27]

    Carl Edward Rasmussen and Christopher K. I. Williams.Gaussian Processes for Machine Learning. The MIT Press, 2005.doi:10.7551/mitpress/3206.001.0001.url:https: //doi.org/10.7551/mitpress/3206.001.0001. 17

    work page doi:10.7551/mitpress/3206.001.0001.url:https: 2005

  28. [28]

    Satellite drag coefficient modeling for thermosphere science and mission operations

    Piyush M Mehta et al. “Satellite drag coefficient modeling for thermosphere science and mission operations”. In:Advances in Space Research(2023)

    work page 2023

  29. [29]

    Modelling of space weather effects on satellite drag

    E Doornbos and H Klinkrad. “Modelling of space weather effects on satellite drag”. In: Advances in Space Research(2006)

    work page 2006

  30. [30]

    Impact of tidal density variability on orbital and reentry predictions

    J. M. Leonard, J. M. Forbes, and G. H. Born. “Impact of tidal density variability on orbital and reentry predictions”. In:Space Weather(2012).doi:https : / / doi . org / 10 . 1029 / 2012SW000842

    work page 2012

  31. [31]

    Satellite orbital drag

    Eftyhia Zesta and Cheryl Y Huang. “Satellite orbital drag”. In:Space weather fundamentals. CRC Press, 2016

    work page 2016

  32. [32]

    Ant´ onia Amaral Turkman, Carlos Daniel Paulino, and Peter M¨ uller.Computational Bayesian Statistics: An Introduction

    M. Ant´ onia Amaral Turkman, Carlos Daniel Paulino, and Peter M¨ uller.Computational Bayesian Statistics: An Introduction. Institute of Mathematical Statistics Textbooks. Cam- bridge University Press, 2019

    work page 2019

  33. [33]

    Piecewise polynomial, positive definite and compactly supported radial functions of minimal degree

    Holger Wendland. “Piecewise polynomial, positive definite and compactly supported radial functions of minimal degree.” In:Adv Comput Math(1995)

    work page 1995

  34. [34]

    Strictly Proper Scoring Rules, Prediction, and Estimation

    T. Gneiting and A. Rafferty. “Strictly Proper Scoring Rules, Prediction, and Estimation”. In:Journal of the American Statistical Association(2007).url:https://doi.org/10. 1198/016214506000001437. [35]NIST Digital Library of Mathematical Functions.https://dlmf.nist.gov/, Release 1.2.5 of 2025-12-15. F. W. J. Olver, A. B. Olde Daalhuis, D. W. Lozier, B. I. ...

    work page 2007

  35. [35]

    XVI. Functions of positive and negative type, and their connection the theory of integral equations

    James Mercer and Andrew Russell Forsyth. “XVI. Functions of positive and negative type, and their connection the theory of integral equations”. In:Philosophical Transactions of the Royal Society of London. Series A, Containing Papers of a Mathematical or Physical Char- acter(1909).doi:10.1098/rsta.1909.0016.url:https://royalsocietypublishing. org/doi/abs/...

    work page doi:10.1098/rsta.1909.0016.url:https://royalsocietypublishing 1909