Index: Pewsey 2021 - Recent Advances in Directional Statistics

Pewsey 2021 - Recent Advances in Directional Statistics

Routing Summary

Captures Pewsey and García-Portugués (2021), Recent advances in directional statistics (TEST 30; arXiv 2005.06889, 61 pp.): circular, toroidal, cylindrical and spherical models, inference and uniformity tests, regression and time-series for angular data, KDE, PCA, classification, spatial models, software. 5 notes plus overview. Motivating PyMC example: E81 (circular data: wind, times of day, seasons).

• Need the one-page summary and source map? → Pewsey 2021 - Directional Statistics - Overview
• Need von Mises, wrapped, projected, cardioid, sine-skewed, Jones-Pewsey, Kato-Jones, mixtures? → Pewsey 2021 - Circular Distributions and Constructions
• Need estimation, Bayesian methods, score matching, smeariness, Rayleigh/Sobolev uniformity tests? → Pewsey 2021 - Inference, Uniformity Tests and Smeariness
• Need tan-half link, projected normal regression, harmonic regression, KDE/NW, circular AR? → Pewsey 2021 - Circular Regression and Serial Dependence
• Need torus/cylinder/sphere models, circulas, PCA, spatial processes, software? → Pewsey 2021 - Directional Statistics - Spherical, Toroidal and Other Topics
• Need PyMC patterns (von Mises with harmonics, wrapped-prior pitfalls)? → Pewsey 2021 - Circular Models in PyMC

Concept Map

Concept	Note	Type	Depends On	Key Result
Von Mises	Pewsey 2021 - Circular Distributions and Constructions	definition	-	$\propto \exp \{\kappa \cos (\theta -\mu )\}$; ML = moments
Wrapping, projection, perturbation	Pewsey 2021 - Circular Distributions and Constructions	definition	vM	WC closed form; sine-skew
Jones-Pewsey, Kato-Jones	Pewsey 2021 - Circular Distributions and Constructions	definition	vM, WC	flexible unimodal
Smeariness	Pewsey 2021 - Inference, Uniformity Tests and Smeariness	definition	intrinsic mean	rate slower than $n^{-1/2}$
Sobolev uniformity tests	Pewsey 2021 - Inference, Uniformity Tests and Smeariness	theorem	-	Rayleigh ($j=1$), Bingham ($j=2$)
Tan-half link, projected-normal regression	Pewsey 2021 - Circular Regression and Serial Dependence	definition	vM	link ML is hard
Circular AR / linked ARMA	Pewsey 2021 - Circular Regression and Serial Dependence	definition	vM	CAR conditional vM
Bivariate vM, circulas	Pewsey 2021 - Directional Statistics - Spherical, Toroidal and Other Topics	definition	vM	binding density, copula link
vMF, Fisher-Bingham	Pewsey 2021 - Directional Statistics - Spherical, Toroidal and Other Topics	definition	vM	$S^d$ analogues
Harmonic vM in PyMC	Pewsey 2021 - Circular Models in PyMC	concept	vM, regression	canonical $(\kappa \cos \mu ,\kappa \sin \mu )$

Notes

• Pewsey 2021 - Directional Statistics - Overview — CONTAINS: question, contribution, E81 link, full source map.
• Pewsey 2021 - Circular Distributions and Constructions — CONTAINS: Defs. vM, wrapping, projection, perturbation, flexible families, mixtures, generalized vM; exploratory plots; Python MLE.
• Pewsey 2021 - Inference, Uniformity Tests and Smeariness — CONTAINS: likelihood/moment/score-matching/Bayesian inference; smeariness; Thm. Sobolev (Eq. 15); Rayleigh Python.
• Pewsey 2021 - Circular Regression and Serial Dependence — CONTAINS: Eq. 16, tan-half link, projected-normal regression, harmonic regression, spherical responses, KDE/NW, circular time series.
• Pewsey 2021 - Directional Statistics - Spherical, Toroidal and Other Topics — CONTAINS: Eqs. 8-14, circulas, cylindrical, vMF/Fisher-Bingham, PCA, classification, spatial, compositional link, software.
• Pewsey 2021 - Circular Models in PyMC — CONTAINS: resultant vector, harmonic vM, projected-normal scaffold, wrapped-prior pitfalls.

Sources

• Pewsey 2021 - Recent Advances in Directional Statistics — Pewsey A, García-Portugués E (2021), TEST 30 (2021); arXiv:2005.06889.

See Also

• Generalized Linear Models, Hilbert Space Gaussian Processes, Local Linear Trend and Seasonality, Factor Copulas - Overview