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arxiv: 1907.07439 · v1 · pith:GGFPOGDEnew · submitted 2019-07-17 · 📊 stat.AP

Spherical data handling and analysis with R package rcosmo

Daniel Fryer , Andriy Olenko This is my paper

Pith reviewed 2026-05-24 20:12 UTC · model grok-4.3

classification 📊 stat.AP
keywords rcosmoHEALPixspherical dataR packageCMBgeographic datapoint patternsstar-shaped data
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The pith

The rcosmo R package converts and analyzes non-CMB spherical data by transforming it into HEALPix format.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper demonstrates that rcosmo, built for cosmic microwave background data, applies to other spherical data types through format conversions. It covers continuous geographic data, point patterns, and star-shaped objects, supplying statistical models, examples, and ready-to-use R code for each. The package's more than 100 functions become available once data enters the HEALPix structure. This setup gives geo-statisticians and GIS users a direct path to leverage existing CMB tools on their own spherical datasets.

Core claim

rcosmo was developed for handling and analysing HEALPix and CMB radiation data with more than 100 functions. It can be used for other spherical data by transforming them into rcosmo formats, with demonstrations for geographic, point pattern and star-shaped data.

What carries the argument

Transformations of non-CMB spherical data into HEALPix format within the rcosmo package

If this is right

  • Geographic data can be fed into rcosmo functions after conversion for standard spherical statistics.
  • Point pattern data on the sphere becomes amenable to the package's existing point-process tools.
  • Star-shaped data sets can undergo the same modeling steps once placed in HEALPix form.

Where Pith is reading between the lines

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

  • The same conversion route might apply to additional spherical data types such as directional measurements or spherical images.
  • Integration with existing GIS software could become simpler if rcosmo conversion routines are exposed as standalone functions.

Load-bearing premise

Converting non-CMB data to HEALPix format preserves the statistical properties needed for valid analysis without significant loss or distortion.

What would settle it

A direct comparison showing that standard statistical measures such as means, variances or spatial correlations change materially after conversion to HEALPix would falsify the claim that the transformations support valid analysis.

Figures

Figures reproduced from arXiv: 1907.07439 by Andriy Olenko, Daniel Fryer.

Figure 1
Figure 1. Figure 1: HEALPix base pixel planar projection as 12 squares. The base pixelation is defined to have the resolution parameter j = 0. For resolution j = 1, each base pixel is subdivided into 4 equiareal child pixels. This process is repeated for higher resolutions with each pixel at resolution j = k being one of 4 child pixels from the subdivision of its parent pixel in resolution j = k − 1. At any resolution j, the … view at source ↗
Figure 2
Figure 2. Figure 2: HEALPix pixelation at resolution j = 1 in ring ordering scheme. 20 19 18 17 36 35 34 33 4 3 2 1 24 23 22 21 40 39 38 37 8 7 6 5 28 27 26 25 44 43 42 41 12 11 10 9 32 31 30 29 48 47 46 45 16 15 14 13 [PITH_FULL_IMAGE:figures/full_fig_p004_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: HEALPix pixelation at resolution j = 1 in nested ordering scheme. 3 Continuous geographic data In this section we demonstrate how rcosmo can be applied to handle contin￾uous geo-references observations. Such observations are usually collected over dense geographic grids or obtained as results of spatial interpolation or smooth￾ing. Continuous geographic data are common in meteorology, for example, maps wit… view at source ↗
Figure 4
Figure 4. Figure 4: Total column ozone map with Australia and China boundaries. > alpha <- mean(cmb[,"I", drop = TRUE]) > alpha [1] 298.4333 > win1 <- CMBWindow(theta = c(0,pi/2,pi/2), phi = c(0,0,pi/2)) > exprob(cmb, win1, alpha,intensities = "I") [1] 0.3557902 > extrCMB(cmb, win1, 3, intensities = "I") A CMBDataFrame # A tibble: 3 x 4 I theta phi I1 <dbl> <dbl> <dbl> <dbl> 1 179. 3.07 3.32 -0.00119 2 180. 2.96 4.21 -0.00119… view at source ↗
Figure 5
Figure 5. Figure 5: Locations of IGRA stations and Australia and China boundaries. As the data are in the HEALPix format a few rcosmo functions were em￾ployed to analyse them. For example, the first Minkowski functional fmf can be used to estimate a relative area of HEALPix locations with the elevation above sea level. > fmf(cmb, 0, intensities = "I")/(dim(cmb)[1]*pixelArea(cmb)) [1] 0.9869792 The minimum angular geodesic dis… view at source ↗
Figure 6
Figure 6. Figure 6: Distribution of the elevation with respect to spherical angles. details on other models and methods in statistical directional and shape analysis can be found in [13] and [15]. In contrast to geographic data in Sections 3 and 4, directional data are not necessarily located on a sphere, but rather are observed in radial directions from a common centre. However, they are usually indexed by points of the unit… view at source ↗
Figure 7
Figure 7. Figure 7: Sampled points of left amygdala surfaces of persons 10 and 13. > pix(cmb1) <- pix(hp1) > cmb1$I1 <- (cmb1$I-mean(cmb1$I))/1000 > plot(cmb1,intensities = "I1",back.col = "white", size = 3, xlab = ’’, ylab = ’’, zlab = ’’) We repeat the same steps for the left amygdala of person 13. The second [PITH_FULL_IMAGE:figures/full_fig_p012_7.png] view at source ↗
Figure 8
Figure 8. Figure 8: Heat maps of ||xi − x0|| for persons 10 and 13. To analyse and compare shapes of the amygdalae we first use directional his￾tograms. For example, [PITH_FULL_IMAGE:figures/full_fig_p012_8.png] view at source ↗
Figure 9
Figure 9. Figure 9: Distributions of sampled points with respect to θ for persons 10 and 13. However, basic statistical analysis of the variable I containing values of the sampled radial distances ||xi −x0|| shows differences in the shapes of the control and autistic cases: Person Mean First Minkowski functional 10 7.525838 0.0003348093 13 8.396525 0.0004266883 [PITH_FULL_IMAGE:figures/full_fig_p013_9.png] view at source ↗
read the original abstract

The R package rcosmo was developed for handling and analysing Hierarchical Equal Area isoLatitude Pixelation(HEALPix) and Cosmic Microwave Background(CMB) radiation data. It has more than 100 functions. rcosmo was initially developed for CMB, but also can be used for other spherical data. This paper discusses transformations into rcosmo formats and handling of three types of non-CMB data: continuous geographic, point pattern and star-shaped. For each type of data we provide a brief description of the corresponding statistical model, data example and ready-to-use R code. Some statistical functionality of rcosmo is demonstrated for the example data converted into the HEALPix format. The paper can serve as the first practical guideline to transforming data into the HEALPix format and statistical analysis with rcosmo for geo-statisticians, GIS and R users and researches dealing with spherical data in non-HEALPix formats.

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

0 major / 3 minor

Summary. The manuscript describes the R package rcosmo (originally developed for HEALPix and CMB data) and its extension to three classes of non-CMB spherical data: continuous geographic, point-pattern, and star-shaped. For each class it supplies a brief statistical-model description, an example dataset, ready-to-use R code that converts the data into HEALPix format, and demonstrations of selected rcosmo statistical functions on the converted data. The paper positions itself as a practical guideline for geo-statisticians, GIS users, and researchers working with spherical data in non-HEALPix formats.

Significance. If the supplied conversion routines and function calls operate as documented, the work supplies a concrete, immediately usable pipeline that lowers the barrier for applying HEALPix-based tools to other spherical data types. The provision of ready-to-run code and example datasets is a concrete strength for reproducibility and adoption.

minor comments (3)
  1. [Abstract] The abstract states that rcosmo “has more than 100 functions” yet never indicates which subset is exercised or recommended for the three non-CMB data types; a short table or explicit list in §2 or §3 would clarify scope.
  2. [Sections 3–5] The descriptions of the statistical models for the three data types are only one paragraph each; adding one or two key equations or references per model would help readers assess whether the subsequent rcosmo analyses are appropriate.
  3. [Figures 1–3] Figure captions and axis labels in the example plots are not described in the text; readers cannot tell which rcosmo function produced each panel without inspecting the accompanying code blocks.

Simulated Author's Rebuttal

0 responses · 0 unresolved

We thank the referee for the careful reading and positive assessment of the manuscript, including the accurate summary of its scope and the recommendation for minor revision. No specific major comments were listed in the report.

Circularity Check

0 steps flagged

No significant circularity identified

full rationale

The paper is a descriptive software guide for the rcosmo R package. It covers data transformations into HEALPix format, brief statistical model descriptions, example datasets, and ready-to-use R code for continuous geographic, point pattern, and star-shaped data. No mathematical derivations, predictions, fitted parameters, or uniqueness theorems are advanced. No self-citations serve as load-bearing premises for any central claim. The content consists of practical pipelines and demonstrations without any reduction of results to inputs by construction.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

No mathematical derivations, free parameters, axioms, or new entities are introduced; the work relies on the pre-existing HEALPix standard and conventional statistical models for the listed data types.

pith-pipeline@v0.9.0 · 5683 in / 1117 out tokens · 25936 ms · 2026-05-24T20:12:56.143814+00:00 · methodology

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Reference graph

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