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A new forecasting method based on the concept of the profile predictive the likelihood function is proposed for discrete-valued processes. In particular, generalized autoregressive and moving average (GARMA) models for Poisson distributed…
In this work we: (1) review likelihood-based inference for parameter estimation and the construction of confidence regions; and, (2) explore the use of techniques from information geometry, including geodesic curves and Riemann scalar…
First, we consider galaxy formation from the viewpoint of hierarchical clustering theory and discuss the possibility that inhomogeneous models with a local void may be compatible with the observed homogeneity of galactic distributions found…
A new two-parameter discrete distribution, namely the PoiG distribution is derived by the convolution of a Poisson variate and an independently distributed geometric random variable. This distribution generalizes both the Poisson and…
We introduce the information geometry module of the Python package Geomstats. The module first implements Fisher-Rao Riemannian manifolds of widely used parametric families of probability distributions, such as normal, gamma, beta,…
Gaussian processes provide a method for extracting cosmological information from observations without assuming a cosmological model. We carry out cosmography -- mapping the time evolution of the cosmic expansion -- in a model-independent…
Mismodeling the uncertain, diffuse emission of Galactic origin can seriously bias the characterization of astrophysical gamma-ray data, particularly in the region of the Inner Milky Way where such emission can make up over 80% of the photon…
Towards formulating quantum gravity, we present a novel mechanism for the emergence of spacetime geometry from randomness. In [arXiv:1705.06097], we defined for a given Markov stochastic process "the distance between configurations," which…
Information geometry is concerned with the application of differential geometry concepts in the study of the parametric spaces of statistical models. When the random variables are independent and identically distributed, the underlying…
Accurate analyses of present and next-generation galaxy surveys require new ways to handle effects of non-linear gravitational structure formation in data. To address these needs we present an extension of our previously developed algorithm…
We perform a statistical study on the distribution and dynamics of voids in the 2dFGRS. Our statistics are tested and calibrated using mock 2dFGRS catalogues. We analyse the dynamics around voids in mock and real 2dFGRS surveys. The…
Starting from the geometrical concept of a 4-dimensional de-Sitter configuration of spheres in Euclidean 3-space and modelling voids in the Universe as spheres, we show that a uniform distribution over this configuration space implies a…
Generalized statistical models of voids and hierarchical structure in cosmology are developed. The often quoted negative binomial model and frequently used thermodynamic model are shown to be special cases of a more general distribution…
The voids between galaxies are identified with the volumes of the Poisson Voronoi tessellation. Two new survival functions for the apparent radii of voids are derived. The sectional normalized area of the Poisson Voronoi tessellation is…
We develop a unified framework for distributed inference, semantic communication, and exploration in spatial networks by integrating stochastic geometry with information geometry - a direction that has not been explored in prior literature.…
This paper presents a new derivation of the Generalized Poisson distribution. This distribution provides a good fit to the evolved, counts-in-cells distribution measured in numerical simulations of hierarchical clustering from Poisson…
The Riemannian geometry of covariance matrices has been essential to several successful applications, in computer vision, biomedical signal and image processing, and radar data processing. For these applications, an important ongoing…
Calculus and geometry are ubiquitous in the theoretical modelling of scientific phenomena, but have historically been very challenging to apply directly to real data as statistics. Diffusion geometry is a new theory that reformulates…
Context. Explaining the accelerated expansion of the Universe is one of the fundamental challenges in physics today. Cosmography provides information about the evolution of the universe derived from measured distances, assuming only that…
Understanding the macroscopic characteristics of biological complexes demands precision and specificity in statistical ensemble modeling. One of the primary challenges in this domain lies in sampling from particular subsets of the…