scholarly journals Multivariate isotropic random fields on spheres: Nonparametric Bayesian modeling and Lp fast approximations

2021 ◽  
Vol 15 (1) ◽  
Author(s):  
Alfredo Alegría ◽  
Pier Giovanni Bissiri ◽  
Galatia Cleanthous ◽  
Emilio Porcu ◽  
Philip White
Keyword(s):  
Random Fields ◽  
Bayesian Modeling ◽  
Nonparametric Bayesian ◽  
Isotropic Random

scholarly journals Needlet approximation for isotropic random fields on the sphere

2017 ◽  
Vol 216 ◽  
pp. 86-116 ◽  
Author(s):  
Quoc T. Le Gia ◽  
Ian H. Sloan ◽  
Yu Guang Wang ◽  
Robert S. Womersley
Keyword(s):  
Random Fields ◽  
Isotropic Random

scholarly journals Identification and isotropy characterization of deformed random fields through excursion sets

2018 ◽  
Vol 50 (3) ◽  
pp. 706-725
Author(s):  
Julie Fournier
Keyword(s):  
Random Field ◽  
Euler Characteristic ◽  
Random Fields ◽  
Weak Form ◽  
Invariance Property ◽  
Basic Domain ◽  
Excursion Sets ◽  
The Mean ◽  
Isotropic Random

Abstract A deterministic application θ:ℝ2→ℝ2 deforms bijectively and regularly the plane and allows the construction of a deformed random field X∘θ:ℝ2→ℝ from a regular, stationary, and isotropic random field X:ℝ2→ℝ. The deformed field X∘θ is, in general, not isotropic (and not even stationary), however, we provide an explicit characterization of the deformations θ that preserve the isotropy. Further assuming that X is Gaussian, we introduce a weak form of isotropy of the field X∘θ, defined by an invariance property of the mean Euler characteristic of some of its excursion sets. We prove that deformed fields satisfying this property are strictly isotropic. In addition, we are able to identify θ, assuming that the mean Euler characteristic of excursion sets of X∘θ over some basic domain is known.

Data-Driven Probabilistic Optimal Power Flow With Nonparametric Bayesian Modeling and Inference

2020 ◽  
Vol 11 (2) ◽  
pp. 1077-1090 ◽  
Author(s):  
Weigao Sun ◽  
Mohsen Zamani ◽  
Mohammad Reza Hesamzadeh ◽  
Hai-Tao Zhang
Keyword(s):  
Bayesian Modeling ◽  
Power Flow ◽  
Optimal Power Flow ◽  
Data Driven ◽  
Nonparametric Bayesian ◽  
Optimal Power
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