Related papers: Bayesian analysis of the backreaction models
In this chapter we provide a thorough overview of the use of energy-based models (EBMs) in the context of inverse imaging problems. EBMs are probability distributions modeled via Gibbs densities $p(x) \propto \exp{-E(x)}$ with an…
In this paper, it is shown that the cosmological model that was introduced in a sequence of three earlier papers under the title, A Dust Universe Solution to the Dark Energy Problem, can be used to resolve the problem of the great mismatch…
In the framework of spatially averaged inhomogeneous cosmologies in classical General Relativity, effective Einstein equations govern the regional and the global dynamics of averaged scalar variables of cosmological models. A particular…
Within the framework of modified gravity model namely Slotheon model, inspired by the theory of extra dimensions, we explore the behaviour of Dark Energy and the perturbations thereof. The Dark Energy and matter perturbations equations are…
We propose a Bayesian inference framework to estimate uncertainties in inverse scattering problems. Given the observed data, the forward model and their uncertainties, we find the posterior distribution over a finite parameter field…
In this paper we study different algorithms for backward stochastic differential equations (BSDE in short) basing on random walk framework for 1-dimensional Brownian motion. Implicit and explicit schemes for both BSDE and reflected BSDE are…
We introduce a methodology for robust Bayesian estimation with robust divergence (e.g., density power divergence or {\gamma}-divergence), indexed by a single tuning parameter. It is well known that the posterior density induced by robust…
In this work we discuss a general approach for the dissipative dark matter considering a nonextensive bulk viscosity and taking into account the role of generalized Friedmann equations. This generalized $\Lambda$CDM model encompasses a flat…
Bayesian imaging inverse problems in astrophysics and cosmology remain challenging, particularly in low-data regimes, due to complex forward operators and the frequent lack of well-motivated priors for non-Gaussian signals. In this paper,…
We study the asymptotic behaviour of the posterior distribution in a broad class of statistical models where the "true" solution occurs on the boundary of the parameter space. We show that in this case Bayesian inference is consistent, and…
Mixture models provide a flexible representation of heterogeneity in a finite number of latent classes. From the Bayesian point of view, Markov Chain Monte Carlo methods provide a way to draw inferences from these models. In particular,…
We study the information content of nuclear masses from the perspective of global models of nuclear binding energies. To this end, we employ a number of statistical methods and diagnostic tools, including Bayesian calibration, Bayesian…
We investigate the relationship between the cosmic curvature and the model of dark energy (hereafter DE) with the recent Type Ia supernovae (hereafter SNe Ia) data, i.e., the Pantheon sample including 1048 SNe Ia with $0.01 < z < 2.3$. We…
Bayesian mixture models are widely used for clustering of high-dimensional data with appropriate uncertainty quantification. However, as the dimension of the observations increases, posterior inference often tends to favor too many or too…
The standard model of cosmology with postulated dark energy and dark matter sources may be considered as a fairly successful fitting model to observational data. However, this model leaves the question of the physical origin of these dark…
For two vast families of mixture distributions and a given prior, we provide unified representations of posterior and predictive distributions. Model applications presented include bivariate mixtures of Gamma distributions labelled as…
We present a formalism for spatial averaging in cosmology applicable to general spacetimes and coordinates, and allowing the easy incorporation of a wide variety of matter sources. We apply this formalism to a…
The backreaction of quantum degrees of freedom on classical backgrounds is a poorly understood topic in theoretical physics. Most often it is treated within the semiclassical approximation with the help of various ad hoc prescriptions…
Recent supernovae of type Ia measurements and other astronomical observations suggest that our universe is in accelerating phase of evolution at the present epoch. While a dark energy of unknown form is usually proposed as the most feasible…
The reconstruction scheme is developed for modified $f(R)$ gravity with realistic matter (dark matter, baryons, radiation). Two versions of such theory are constructed: the first one describes the sequence of radiation and matter…