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  "Title": "Multi-Resolution Thin-Plate Splines on the Sphere",
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  "Authors@R": "c(\nperson(given = \"Hao-Yun\", family = \"Huang\", role = c(\"aut\", \"cre\"),\nemail = \"hhuscout@gmail.com\",\ncomment = c(ORCID = \"0009-0004-8384-3261\")),\nperson(given = \"Hsin-Cheng\", family = \"Huang\", role = \"aut\",\ncomment = c(ORCID = \"0000-0002-5613-349X\")),\nperson(given = \"Ching-Kang\", family = \"Ing\", role = \"aut\",\ncomment = c(ORCID = \"0000-0003-1362-8246\")))",
  "Description": "Constructs multi-resolution thin-plate spline (MRTS) basis\nfunctions on the sphere and fits the corresponding\nmulti-resolution mixed model (MRMM) by generalised least\nsquares with a tapered Matérn residual covariance, including\nkriging-style prediction with closed-form standard errors.\nImplements the system described in Huang, Huang, and Ing (2025)\n\"Multi-Resolution Spatial Methods on the Sphere: Efficient\nPrediction for Global Data\", Environmetrics,\n<doi:10.1002/env.70092>. Heavy basis computations are written\nin 'C++' via 'Rcpp' with optional 'OpenMP' parallelism.",
  "License": "GPL (>= 2)",
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  "URL": "https://github.com/STLABTW/multi-resolution-sphere",
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  "Date/Publication": "2026-05-01 08:24:18 UTC",
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    "id": "206bccb5d8ddaf0f5cd56b31c93cf31121e18d11",
    "author": "Hao-Yun Huang <hhuscout@gmail.com>",
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    "message": "mrtsSphere 0.2.0: add MRMM fit + predict\n\nThe 0.1.x line shipped only the basis-construction step (`mrts_sphere`),\nwhich left users to write the GLS step (the actual modelling part of\nthe paper) themselves. 0.2.0 adds it.\n\nNew exports:\n\n- `mrmm_fit(z, loc, knots, k, taper_range, matern_range, sill, nugget,\n  smoothness)` — fits the multi-resolution mixed model by GLS using a\n  tapered-Matérn residual covariance built from the user-supplied\n  parameters. Returns an S3 `\"mrmm\"` object holding the GLS coefficient,\n  fitted values, residuals, the (B' Sigma^{-1} B)^{-1} matrix needed\n  for prediction SE, and the upper-triangular Cholesky of Sigma so\n  triangular solves can be reused at predict time.\n- `predict.mrmm(object, newdata, se.fit = TRUE)` — kriging-style mean\n  prediction plus closed-form prediction standard error.\n- `tapered_matern_sphere(loc1, loc2, taper_range, matern_range, ...)` —\n  exported helper that returns\n  `sill * Matern(d; c, nu) * Wendland(d; a) + nugget * I` on the unit\n  sphere, with `d` the great-circle distance in radians.\n- `print.mrmm()` for human-readable summaries.\n\nImplementation notes:\n\n- All linear algebra is base R + dense matrices, factorising Sigma\n  once via `chol()` and reusing the factor for every triangular solve.\n  This is a deliberate v0.2.0 simplification — practical training size\n  is comfortable up to a few thousand points; sparse / Matrix support\n  can come later if there is demand.\n- Avoids `pmin`/`pmax` against scalars in `gcdist_sphere()` because they\n  silently strip the matrix `dim` attribute when the first argument is\n  a scalar; uses direct `[ <- ]` indexing instead.\n- Wendland C^2 (k = 2, dim = 2) taper closed form\n  `(1 - r)^6 * (35/3 r^2 + 6 r + 1)` for r <= 1, 0 outside; matches\n  what `fields::Wendland(theta = a, k = 2, dimension = 2)` returns\n  and what the original paper script uses.\n- Matern correlation uses `besselK()`; takes the closed-form\n  `exp(-d / range)` shortcut when smoothness is 0.5.\n\nA future relea",
    "time": 1777623858
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      "week": "2026-13",
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