Related papers: II: Bayesian Methods for Cosmological Parameter Es…
The Metropolis algorithm is a Markov chain Monte Carlo (MCMC) algorithm used to simulate from parameter distributions of interest, such as generalized linear model parameters. The "Metropolis step" is a keystone concept that underlies…
We analyze the spectrum of cosmic microwave background (CMB) anisotropies in the timescape cosmology: a potentially viable alternative to homogeneous isotropic cosmologies without dark energy. We exploit the fact that the timescape…
Cosmological probes pose an inverse problem where the measurement result is obtained through observations, and the objective is to infer values of model parameters which characterize the underlying physical system -- our Universe. Modern…
In this paper we develop the theory of clusterization of peaks in a Gaussian random field. We have obtained new mathematical results from this theory and the theory of percolation and have proposed a topological method of analysis of sky…
The posterior probability distribution for a set of model parameters encodes all that the data have to tell us in the context of a given model; it is the fundamental quantity for Bayesian parameter estimation. In order to infer the…
In this paper, we present the first study that compares different models of Bayesian Neural Networks (BNNs) to predict the posterior distribution of the cosmological parameters directly from the Cosmic Microwave Background temperature and…
Non-Gaussian distributions in cosmology are commonly evaluated with Monte Carlo Markov-chain methods, as the Fisher-matrix formalism is restricted to the Gaussian case. The Metropolis-Hastings algorithm will provide samples from the…
In this thesis we investigate several aspects related to the theory of fluctuations in the Cosmic Microwave Background. We develop a new algorithm to calculate the angular power spectrum of the anisotropies which is two orders of magnitude…
We introduce an exact Bayesian approach to search for non-Gaussianity of local type in Cosmic Microwave Background (CMB) radiation data. Using simulated CMB temperature maps, the newly developed technique is compared against the…
We present a Bayesian approach to estimate the parameters of mathematical models of cardiac electrophysiology with quantified uncertainty. Such models capture the dynamics of the electrical signal that coordinates the muscle cell…
The recent measurements of the power spectrum of Cosmic Microwave Background anisotropies are consistent with the simplest inflationary scenario and big bang nucleosynthesis constraints. However, these results rely on the assumption of a…
Determining the physical characteristics of a star is an inverse problem consisting in estimating the parameters of models for the stellar structure and evolution, knowing certain observable quantities. We use a Bayesian approach to solve…
We review the topic of Cosmic Microwave Background Anisotropy measurements carried out by means of balloon-borne telescopes. After a short description of the experimental methodology, we outline the peculiar problems of these experiments,…
In this study the common least-squares minimization approach is compared to the Bayesian updating procedure. In the content of material parameter identification the posterior parameter density function is obtained from its prior and the…
For several decades now, Bayesian inference techniques have been applied to theories of particle physics, cosmology and astrophysics to obtain the probability density functions of their free parameters. In this study, we review and compare…
We describe regularized methods for image reconstruction and focus on the question of hyperparameter and instrument parameter estimation, i.e. unsupervised and myopic problems. We developed a Bayesian framework that is based on the \post…
The recent high-quality measurements of the Cosmic Microwave Background anisotropies have presented cosmologists with the possibility of studying the large scale properties of our universe with unprecedented precision. Here I review the…
We constrain the thermal evolution of the universe with a decaying cosmological term by using the method of the analysis for the Wilkinson Microwave Anisotropy Probe (WMAP) observation data. The cosmological term is assumed to be a function…
The Markov chain Monte Carlo method (MCMC), especially the Metropolis-Hastings (MH) algorithm, is a widely used technique for sampling from a target probability distribution $P$ on a state space $\Omega$ and applied to various problems such…
We present a multifrequency approach which optimizes the constraints on cosmological parameters with respect to extragalactic sources and secondary anisotropies contamination on small scales. We model with a minimal number of parameters the…