Related papers: A Test for Isotropy on a Sphere using Spherical Ha…
An important aspect of modeling spatially-referenced data is appropriately specifying the covariance function of the random field. A practitioner working with spatial data is presented a number of choices regarding the structure of the…
The cosmological principle is fundamental to the standard cosmological model. It assumes that the Universe is homogeneous and isotropic on very large scales. As the basic assumption, it must stand the test of various observations. In this…
An important step of modeling spatially-referenced data is appropriately specifying the second order properties of the random field. A scientist developing a model for spatial data has a number of options regarding the nature of the…
In spatial statistics, point processes are often assumed to be isotropic meaning that their distribution is invariant under rotations. Statistical tests for the null hypothesis of isotropy found in the literature are based either on…
Several hypothesis testing methods have been proposed to validate the assumption of isotropy in spatial point patterns. A majority of these methods are characterised by an unknown distribution of the test statistic under the null hypothesis…
Rapid developments in satellite remote-sensing technology have enabled the collection of geospatial data on a global scale, hence increasing the need for covariance functions that can capture spatial dependence on spherical domains. We…
We investigate distributional properties of a class of spectral spatial statistics under irregular sampling of a random field that is defined on $\mathbb{R}^d$, and use this to obtain a test for isotropy. Within this context, edge effects…
We address the problem of estimating the spherical-harmonic power spectrum of a statistically isotropic scalar signal from noise-contaminated data on a region of the unit sphere. Three different methods of spectral estimation are…
The standard models of inflation predict statistically homogeneous and isotropic primordial fluc- tuations, which should be tested by observations. In this paper we test the statistical isotropy of the mean of the CMB temperature…
The cosmological principle asserts that the Universe is homogeneous and isotropic on large enough scales. However, alternative cosmological models can bring about anisotropies through local inhomogeneities, anisotropic evolution, or exotic…
Recent observational analyses have suggested possible evidence of hemisphere asymmetry in cosmological datasets. Parameterizations of this kind place observers in a privileged position-specifically on the plane that divides the two…
Identifying an appropriate covariance function is one of the primary interests in spatial and spatio-temporal statistics because it allows researchers to analyze the dependence structure of the random process. For this purpose, spatial…
This paper proposes parametric and non-parametric hypothesis testing algorithms for detecting anisotropy -- rotational variance of the covariance function in random fields. Both algorithms are based on resampling mechanisms, which enable…
This paper discusses sparse isotropic regularization for a random field on the unit sphere $\mathbb{S}^2$ in $\mathbb{R}^{3}$, where the field is expanded in terms of a spherical harmonic basis. A key feature is that the norm used in the…
The two fundamental assumptions in cosmology are that the Universe is statistically homogeneous and isotropic when averaged on large scales. Given the big implication of these assumptions, there has been a lot of statistical tests carried…
We propose a novel method for testing isotropy of a three-dimensional distribution using Shannon entropy. We test the method on some Monte Carlo simulations of isotropic and anisotropic distributions and find that the method can effectively…
We test the isotropy of the local distribution of galaxies using the 2MASS extended source catalogue. By decomposing the full sky survey into distinct patches and using a combination of photometric and spectroscopic redshift data, we use…
The assumption of homogeneity and isotropy on large scales is one of the main hypotheses of the standard cosmological model. In this paper, we revisit a test of cosmological isotropy using type Ia supernova (SN Ia) distances provided by the…
A spatial point pattern is called anisotropic if its spatial structure depends on direction. Several methods for anisotropy analysis have been introduced in the literature. In this paper, we give an overview of nonparametric methods for…
When searching for deviations of statistical isotropy in CMB, a popular strategy is to write the two-point correlation function (2pcf) as the most general function of four spherical angles (i.e., two unit vectors) in the celestial sphere.…