Stochastic homology of Gaussian vs. non-Gaussian random fields: graphs towards Betti numbers and persistence diagrams

Analysis of Betti Numbers and Persistence Diagrams of 2-Dimensional Gaussian Random Fields

In order to unravel the high-energy physics of the early universe, several methods have been proposed to study the Cosmic Microwave Background (CMB). Current methods have posed bounds on the strength of non-Gaussianities in the CMB, but have so far not succeeded in constraining inflationary physics [8, 37, 23, 2, 38, 6, 21, 24]. This is one of the major open problems in cosmology and particle p...

Numerical Simulation of Non-Gaussian Random Fields

The non-Gaussian random fields are used to modelling some dynamic loads generated by wind turbulence, ocean waves, earthquake ground motion etc. These fields also represent the uncertain properties of different materials (reinforced concrete, composite, soils etc.). This paper presents some methods and the corresponding algorithms to the numerical simulation of stationary non-Gaussian random fi...

Autoregressive Gaussian Random Vectors of First Order

Skew-Gaussian Random Fields

Skewness is often present in a wide range of spatial prediction problems, and modeling it in the spatial context remains a challenging problem. In this study a skew-Gaussian random field is considered. The skew-Gaussian random field is constructed by using the multivariate closed skew-normal distribution, which is a generalization of the traditional normal distribution. We present an Metropolis...

Gaussian Process Random Fields

Gaussian processes have been successful in both supervised and unsupervised machine learning tasks, but their computational complexity has constrained practical applications. We introduce a new approximation for large-scale Gaussian processes, the Gaussian Process Random Field (GPRF), in which local GPs are coupled via pairwise potentials. The GPRF likelihood is a simple, tractable, and paralle...