Related papers: II: Bayesian Methods for Cosmological Parameter Es…
The CMB anisotropy depends sensitively upon the slope and amplitude of primordial density and gravitational wave fluctuations, the baryon density, the Hubble constant, the cosmological constant, the ionization history, {\it etc.} We report…
Traditional Markov Chain Monte Carlo methods suffer from low acceptance rate, slow mixing and low efficiency in high dimensions. Hamiltonian Monte Carlo resolves this issue by avoiding the random walk. Hamiltonian Monte Carlo (HMC) is a…
Monte-Carlo techniques are standard numerical tools for exploring non-Gaussian and multivariate likelihoods. Many variants of the original Metropolis-Hastings algorithm have been proposed to increase the sampling efficiency. Motivated by…
Recently funded satellites will map the cosmic microwave background radiation with unprecedented sensitivities and angular resolutions. Assuming only primordial adiabatic scalar and tensor perturbations, we evaluate how accurately…
Cosmic microwave background (CMB) anisotropy is our richest source of cosmological information; the standard cosmological model was largely established thanks to study of the temperature anisotropies. By the end of the decade, the Planck…
We introduce a simple yet powerful {\it analytic} method which obtains the structure of cosmic microwave background anisotropies to better than 5-10\% in temperature fluctuations on {\it all} scales. It is applicable to {\it any} model in…
We briefly review certain aspects of cosmic microwave background anisotropies as generated in passive and active models of structure formation. We then focus on cosmic strings based models and discuss their status in the light of current…
The Planck satellite, along with several ground based telescopes, have mapped the cosmic microwave background (CMB) at sufficient resolution and signal-to-noise so as to allow a detection of the subtle distortions due to the gravitational…
In the first part of this work, I review the theoretical framework of cosmological perturbation theory necessary to understand the generation and evolution of cosmic microwave background (CMB) anisotropies. Using analytical and numerical…
The Cosmic Microwave Background (CMB) is an abundant source of cosmological information. However, this information is encoded in non-trivial ways in a signal that is difficult to observe. The resulting challenges in extracting this…
The angular power spectrum of the cosmic microwave background (CMB) contains information on virtually all cosmological parameters of interest, including the geometry of the Universe ($\Omega$), the baryon density, the Hubble constant ($h$),…
We are now beginning to learn detailed information about cosmological parameters from the shapes of the matter and radiation power spectra, together with their relative normalization. As more high quality data are gathered from galaxy…
We use a high-accuracy computational code to investigate the precision with which cosmological parameters could be reconstructed by future cosmic microwave background (CMB) experiments, in particular the two satellite missions MAP and…
Motivated by Bayesian inference with highly informative data we analyze the performance of random walk-like Metropolis-Hastings algorithms for approximate sampling of increasingly concentrating target distributions. We focus on Gaussian…
We present a new method for calculating linear cosmic microwave background (CMB) anisotropy spectra based on integration over sources along the photon past light cone. In this approach the temperature anisotropy is written as a time…
We introduce a statistical measure of the effective model complexity, called the Bayesian complexity. We demonstrate that the Bayesian complexity can be used to assess how many effective parameters a set of data can support and that it is a…
We introduce a new technique to detect the discrete temperature steps that cosmic strings might have left in the cosmic microwave background (CMB) anisotropy map. The technique provides a validity test on the pattern search of cosmic…
We present the public release of the Bayesian sampling algorithm for cosmology, CosmoPMC (Cosmology Population Monte Carlo). CosmoPMC explores the parameter space of various cosmological probes, and also provides a robust estimate of the…
The last years have been an exciting period for the field of the Cosmic Microwave Background (CMB) research. With recent CMB balloon-borne and ground-based experiments we are entering a new era of 'precision' cosmology that enables us to…
We consider generalizations of the classical inverse problem to Bayesien type estimators, where the result is not one optimal parameter but an optimal probability distribution in parameter space. The practical computational tool to compute…